--- title: Principia url: https://annotestimonii.com/principia updated: 2026-10-03 --- > How this was checked: https://annotestimonii.com/record.md · Fingerprints of everything published: https://annotestimonii.com/changelog.md # Principia Everything the house has found, on four shelves. Each card says what was claimed and how far it has been checked. The shelves take their names from Newton: propositions and scholia from his Principia, queries from his Opticks. I Propositions What we stand on 18 cards II Queries Open tests 13 cards III Scholia Readings 12 cards IV Errata What didn’t hold 15 cards I Propositions · What we stand on These results have been checked, and each card says how. Two skeptics, one for the mathematics and one for the meaning, re-derived and re-ran these on their own: the four pipes (Register 72 and 73), the mathematics of The Return (Register 75), the 34 results found again, and the fold on a turn that is watched without being read. The house's own pre-registered tests (Register 25, 26, 29, 30, 31, 32, 39, 45, 47, 50, 59 and 67) were checked again, independently; 25, 26, 29, 30 and 31 by a second session's own code. Register 20 is a derivation, with no independent check recorded. Register 61 is a room resting on entry 59's test, checked again, independently. No skeptic checked those. Register 70 is a count of the house's own data. Register 71 is a search of the literature. Many results were found again: the same mathematics was already in print, in another field, and the card names it. Others are the house's own. 'Proven' is used only for a pipe that passed both skeptics. Faith is priced, and faith lifts (The Ledger + Faith and Belief) Waiting is a relay (Drift + Testimony) Reading in step with a swing hides the swing (Noise and Drag + The False Rhythm) A running average settles fastest at a middle drag (Noise and Drag + Position) The Return: circling the truth turns by Newton's angle The rooms' equations turn up again in 34 published results Watching without reading: an observer's noise holds a turn One system of choice: 42 landings on older mathematics, 41 of them placed in 24 fields What is new, after a search of the literature Agreeing witnesses add like speeds Faith is one more witness Expectation is faith times belief No shape of the pull removes the bottom Nine of the house's flow numbers come from three constants Without faith, a turn made in the dark cannot be seen The scorecard cannot see a counterfeit, so the reference must come from outside The top holds about 665 times harder than the bottom Forty-five degrees: where sharing an aim stops guaranteeing company proven Faith is priced, and faith lifts (The Ledger + Faith and Belief) A system resting at the bottom is charged for facing away. The Ledger pays for facing, not for faith. Faith sets the size of the charge. But faith times belief also lifts the bottom toward the ridge. So the charge does not keep rising as faith grows. It peaks just before the tipping point, then falls. Past the tipping point the bottom is gone, and a system holding the same faith is paid for facing toward. Near the tipping point, more faith costs less: the lift outruns the price. Status proven (passed both skeptics, mathematics and meaning; the one new pipe of the 424-pair round, Register 73). The house's own: neither room says it alone. Not searched as a literature claim. The live figure · Faith is priced, and faith lifts Lean 0.1125: the mind rests at −0.752, facing away. Charged 0.0846 × R·G/b a cycle for facing away. The most it is ever charged. Open it The mathematics At a steady bottom rest x_b(h), h = b₀·b below h_c, the faith charge is R·G·b₀·|x_b| = (R·G/b)·Φ(h), Φ(h) = h·|x_b(h)|. Its peak solves (T + F)(x) + x·(T + F)′(x) = 0 on the bottom branch: x = −0.7517022, h = 0.1125689 = 0.9525260·h_c, Φ = 0.0846183. At h_c = 0.118179, Φ = 0.0785822 (7.133% lower). Past h_c the system is paid R·G·0.9973 a cycle facing toward. How it was checked Math skeptic: every number re-derived at 40 digits, and the Ledger run on the settled aim, matching to 10⁻¹⁴ at b = 1, 0.25 and 3. Meaning skeptic could not break it and asked for one change of words (made: the Ledger pays for facing, not for faith). Re-derived independently: x_peak = −0.7517022321, h_peak = 0.1125689034, Φ_peak = 0.08461829598, Φ(h_c) = 0.07858223944, one sign change on the bottom branch, the top at 0.99731744 just past the threshold. Why both rooms are needed: the Ledger alone, aim held at the bottom, rises the whole way (0.1075 against 0.0802 at 0.999 of the threshold); Faith and Belief alone has no price. A generic fold would put the peak at 0.1097; the house's lopsided well puts it at 0.1126. The one new pipe of the full round: 424 pairs worked (Register 73). Sources and run files /house (live data) (TOG pipe 30, [ledger, hope]) the Register ( /letters/witness/ ) (entry 73, batch 5-22) _build/gaps/PIPES_batch-5-22_2026-10-01.md Run files _build/gaps/PIPES_batch-5-22_2026-10-01.md (not served; the Register's entry 73 carries the numbers) What would refute it Within its scope (rest points, a steady aim, belief held fixed, faith at or above zero, R, G and K constant, k = 1, p = 0.35, C = 0.018975): a faith charge that rises all the way to the tipping point, or peaks away from 95.25% of it. On a real system it needs an operational faith, belief and position first, which waits on the author's ruling on Position. See it The pipe: The Ledger + Faith and Belief The house: The Ledger The house: Faith and Belief The Register, entry 73 The geometry: Faith is priced, and faith lifts proven Waiting is a relay (Drift + Testimony) An instrument left to drift testifies like a witness heard through one relay. The relay loses the same share of its strength for each unit of time it drifts. Waiting adds up the way relays do. No chain of relays can win strength back. Turning the instrument back does not either. Only a separate witness from outside can. Status proven (passed both skeptics, mathematics and meaning, Register 72). Craig (1699) described the same fading in words (cited, not reproduced). The same shape appears in a qubit's yes-or-no readout under noise and in a heading that drifts in the dark (shared mathematics only). The pipe joining the two rooms is the house's. The mathematics r(t) = e^(−(d−1)Dt), with Drift's own rate D; the drifted instrument is right (1 + x₀·r(t))/2 of the time; r(t₁)·r(t₂) = r(t₁ + t₂); holding a belief X from independent drifted witnesses takes N ≥ artanh X / artanh(x₀·r(t)) of them. Only the first rung of Drift's ladder reaches the reading. How it was checked 200,000 drifting instruments in 2, 3 and 5 dimensions: right-rates within 0.002 of the prediction at every time; relay(0.2) × relay(0.4) = 0.5503 against relay(0.6) = 0.5482 (theory 0.5488); three drifted witnesses who agree: 0.9948 right, predicted 0.9948 (124,101 cases). Both skeptics re-derived it: the cosine is the first harmonic of rotational diffusion and Testimony's reading is linear in the alignment, so averaging over the drift is exact. Independent check: mean cosine within 0.0022 of e^(−(d−1)Dt) in every case. Sources and run files /house (live data) (TOG pipe 27) the Register ( /letters/witness/ ) (entries 71, 72) Run files not published as a data file; the Register's entry 72 carries the checks What would refute it Independent drifted instruments whose right-rate departs from (1 + x₀·e^(−(d−1)Dt))/2, or any chain of relays that raises alignment. Scope: each witness drifts independently. See it The pipe: Drift + Testimony The Register, entry 72 proven Reading in step with a swing hides the swing (Noise and Drag + The False Rhythm) A system that coasts swings back and forth where it rests. Read it exactly once per swing, and the swing vanishes from the readings. They look like the readings of a system that does not coast at all. That look-alike seems to have far more drag than the real one. Its resting odds still read right. Its drift reads wrong. Status proven (passed both skeptics, mathematics and meaning, Register 72). The house's own; not searched as a literature claim. The live figure · Coasting, drag, and climbing out Drag 0.5: mean time to climb out 238.6. The fastest climb. Open it The mathematics Sampled once per period, the damped swing's correlation falls as e^(−(γ/2m)·t), which is a non-coasting system's exactly when its drag is 2·m·κ/γ (inertia m, stiffness κ, drag γ). How it was checked Exact covariance at a clock of one swing and of two: identical to the non-coasting system to 3×10⁻¹⁵. Read four times per swing, the swing shows (difference 0.53). A simulation of 60,000 readings read the drag as 4.95 against the predicted 5.00 (true 0.40); a skeptic's own exact run read 5.02. In the check, drift read 0.10 against 1.25 true. On the house's lopsided bottom well the drag reads about 2% low. Sources and run files /house (live data) (TOG pipe 28) the Register ( /letters/witness/ ) (entry 72) Run files not published as a data file; the Register's entry 72 carries the checks What would refute it Readings locked to the swing period that can be told apart from a non-coasting system's, or a drag read that does not approach 2mκ/γ. Scope: exact only when the clock locks to the swing. See it The pipe: Noise and Drag + The False Rhythm The Register, entry 72 The geometry: Coasting, drag, and climbing out proven A running average settles fastest at a middle drag (Noise and Drag + Position) Position is the running average of how a system faces. It settles at the same place whatever the system's inertia or drag. How fast it settles depends on both. It settles fastest at a middle amount of drag. Coasting freely is slower. So is being all drag. More inertia settles more slowly, even at its best drag. Status proven (passed both skeptics, mathematics and meaning, Register 72). The house's own; not searched as a literature claim. The mathematics Leftover variance after a long body time t: v²·[m/(2γ) + γ/(2κ)]/t, v² the resting variance of the angle; least at γ = √(m·κ), where it grows as √m. How it was checked Closed form matches direct integration to 6 digits at 6 settings. Simulation, inertia 4: the drag scan's minimum falls at drag 2, as predicted (5.2×10⁻³ against 1.1×10⁻² and 1.2×10⁻² at the ends). As the noise goes to zero, simulation over prediction goes to 0.99. At the room's own noise the numbers are off by 2 to 3 times, and the pattern holds. Sources and run files /house (live data) (TOG pipe 29) the Register ( /letters/witness/ ) (entry 72) Run files not published as a data file; the Register's entry 72 carries the checks What would refute it A drag scan whose least leftover wobble sits away from √(m·κ) as the noise goes to zero. Scope: Position read as the running average, cycles dense in body time. See it The pipe: Noise and Drag + Position The Register, entry 72 lands The Return: circling the truth turns by Newton's angle A system with choice can circle the truth. It does not only turn toward it or away from it. While it circles, it never faces the truth head on. It swings in close and out far. Each swing carries it part of the way around. Newton worked out this turn in 1687, for paths that are nearly round. A swing that stays facing the truth turns between a quarter and a half of the way around. A swing that crosses into facing away turns between a half and three quarters. The mathematics is shared only. A system with choice is not a planet. This room is about circling. It forecasts nothing. Status lands (room 50, Register 75). Two skeptics confirmed the mathematics; neither promoted it as a room. The restatement skeptic voted fold; the landing skeptic left room or fold to the author. It is a room by the author's ruling of 2 October. Found again: Newton (1687), Puiseux (1842), Airy (1851), Liebmann (1903). The crossing bound, a half to three quarters of the way around, is the house's own proof; it was in none of the sources opened, but no wider search was run, so it is not claimed as new. The live figure · The Return: circling the truth Each swing turns 124.81° around the truth, from nearest to farthest. It stays facing, so it turns between 90° and 180° (Puiseux). Newton’s rule for a nearly round path with the same circling: 124.81°. They agree. Open it The mathematics The turning momentum ℓ = m·sin²θ·(turn rate about L̂) is kept, so θ never reaches 0 while ℓ ≠ 0. Facing: mθ̈ = ℓ²cos θ/(m sin³θ) − R·G·sin θ. Facing away: mθ̈ = ℓ²cos θ/(m sin³θ). Nearly round at θ₀: Ψ = π/√(1 + 3cos²θ₀), Newton's 180°/√index with index 1 + 3cos²θ₀. Facing swings: 90° < Ψ < 180° (Puiseux). Crossing swings: 180° < Ψ < 270°. A small oval: Ψ = π/2 + (3π/16)·θ₁·θ₂ (Airy). A path closes exactly when Ψ/π is a ratio of whole numbers; the far point moves 2Ψ − 360° per swing. How it was checked Controls read 90.0000000000° (the sphere's Hooke law) and 180.0000000000° (its Kepler law). At 40 digits: 170.084012802° against the formula's 170.084012854° at cos θ₀ = 0.2, and 124.807543877° against 124.807544151° at 0.6. Airy ratios 1.00005 to 1.0058. All 1,770 facing swings fell inside (90°, 180°) and all 3,600 crossing swings inside (180°, 270°). The crossing bound is proved: the lower edge because g(u_max) > g(u), the upper by concavity against the sphere's Kepler law. Closing paths: a 120° swing returns after 6 legs (gap 4.5×10⁻¹²), a 225° swing after 8 (gap 1.4×10⁻¹⁰). In five dimensions Ψ = 105.272415186° ± 1.4×10⁻¹⁰° over 41 legs, the aim staying in its 3-D span to 2.9×10⁻¹⁵. An independent builder integration: 124.8076° against the formula's 124.8075° at cos θ₀ = 0.6. One surveyor and two skeptics (workflow wf_bd0c1ed0-a4e). Both skeptics confirmed the mathematics. The restatement skeptic derived the swing from the Action's own Lagrangian (sympy difference 0) and voted fold; the landing skeptic required Newton's condition (nearly round paths) and left room or fold to the author. The author ruled it a room on 2 October, because the Action turns only toward and away. With this room the coincidence count went to 1 in 10¹⁴⁹ (rooms only: 1 in 10¹³⁹; see "What the count measures"). Sources and run files Newton, Principia I, Sec. IX, Prop. 45, Ex. 2 (Bruce translation, opened) Puiseux, J. Math. Pures Appl. 7 (1842) 517–520 (opened) Airy 1851, as quoted in arXiv 2502.12230 Liebmann 1903, via Diacu, Pérez-Chavela and Santoprete, arXiv 0807.1747 (opened) Ballesteros et al., CMP 290 (2009) 1033 (abstract) /house (live data): ROOMS id newton the Register ( /letters/witness/ ): entry 75 Run files /letters/witness/tested/NEWTON_survey_route_A_result_2026-10-02.json /letters/witness/tested/NEWTON_survey_route_A_check2_2026-10-02.json /letters/witness/tested/NEWTON_vet_landing_bound_proof_check_2026-10-02.json /letters/witness/tested/NEWTON_vet_restatement_vet_elliptic_2026-10-02.json _build/gaps/NEWTON_2026-10-02/ (37 files, 20 of them JSON, under survey/, vet_landing/ and vet_restatement/, plus newton_result.json and promote_newton.py; 14 NEWTON_*.json data files are published in /letters/witness/tested/) What would refute it A facing swing outside 90° to 180°; a crossing swing outside 180° to 270°; a nearly round swing off π/√(1 + 3cos²θ₀) beyond integration error; controls not reading exactly 90° and 180°; or an aim leaving its 3-D span in higher dimensions. It falls back to a fold in The Action if the Action is ruled to already include turning about the truth. See it The house: The Return The house: The Action The Register, entry 75 The geometry: The Return: circling the truth found again The rooms' equations turn up again in 34 published results Each room has its own landing. Beyond that, the rooms' equations reproduce more published results from other fields. There are 34 so far. Each one is forced by its room's equation, not just cited. Bell's classical limit and Tsirelson's bound come out of one room. Condorcet's jury theorem and the error-correcting codes in 5G, Wi-Fi 6 and satellite-TV decoders come out of another. Six candidates were dropped because they were only cited, or true by construction. Shared mathematics only: a system with choice is not a quantum particle. Status found again (34 results in 28 folds), each forced by its room's equation and checked by skeptics in batches of 8 or fewer, with a critic for completeness (workflow wf_dbae641b-6d0). Each is counted at a coin toss in the house's committed count, by the author's ruling of 1 October. The live figure · Witnesses, and the speed of light 5 witnesses at 0.30: side by side 0.9134, down a chain 0.0024, naive sum 1.5000 (past certainty). Short of certainty by 0.0866. Open it The live figure · The Stake: how much to commit Right 65% of the time, wrong 35%. Best stake: 0.30 of your value. Growth per act: 4.57%. Open it The mathematics Rule (1 October): a fold counts if it reproduces a named published result with the house's own mathematics, forced by its room's equation; one per equation checked within a fold, again in each new field; a citation, a room's own landing, or a result that enters no room does not count. How it was checked The 34, with years, are listed in the house's data: e.g. Bell 1964, Tsirelson 1980, Leggett–Garg 1985, Gallego et al. 2010 (Two Held to One); Fisher 1930 (The Action); Fisher information 1925/1945 and Jaynes 1957 (The Measure); Condorcet 1785, Laplace 1814, Wald 1945, LDPC 1962/2001, Glaze 2015, Ising, Zeno 1977/1990, Born 1926, Kochen–Specker 1967, von Neumann's noisy vote 1956, Bunn–Hogg 2009 (Testimony); Little 1961 (Pressure); Birkhoff 1931 (Position); Krichevsky–Trofimov 1981, Shtarkov 1987, Cover 1991 (The Stake); Asmussen 1989 (Running Dry). Dropped as cited or by construction: Cauchy–Schwarz, Noether, Liouville, Gibbard–Satterthwaite, the central limit theorem, Kira–Yang–Shadlen. Workflow wf_dbae641b-6d0. Shared mathematics only: a system with choice is not a quantum particle. Two were checked again from scratch on 1 October, and two skeptics voted each a fold, not a new room. The quantum Zeno effect (Testimony): an exact two-level calculation, the formula and a 200,000-run reset simulation agree at 0.250000, 0.530790, 0.733133, 0.856877 and 0.925763 for N = 4 to 64 readings of a half turn; about 5,000 Be⁺ ions read 1 to 64 times during a half turn agreed reasonably well with ½[1 − cosⁿ(π/n)] (Itano et al. 1990). Von Neumann's noisy vote (Testimony, with a pointer in Retention): a three-way vote errs 3ε² − 2ε³ of the time (0.000298 at ε = 0.01, by enumeration and by simulation); a stack of three-way votes keeps nothing once each vote fails 1 time in 6 or more (root 0.166667); a five-way vote holds up to 7/30 (Evans and Schulman 2003); Google's chip cut its error per cycle 2.14 ± 0.02 times each time its code distance rose by two. Sources and run files /house (live data) (CLIMB.second_names.list) _build/gaps/ODDS_SECOND_NAMES_2026-10-01.json Itano, 'Perspectives on the quantum Zeno paradox', arXiv quant-ph/0612187 (opened) Misra and Sudarshan, J. Math. Phys. 18, 756 (1977) Itano, Heinzen, Bollinger and Wineland, PRA 41, 2295 (1990) Google Quantum AI, Nature 638, 920 (2025), arXiv 2408.13687 (opened) Aharonov and Ben-Or, arXiv quant-ph/9611025 (opened) Evans and Schulman, Theorem 1 (opened by a skeptic) Hajek and Weller, IEEE Trans. Inf. Theory 37, 388 (1991) _build/gaps/RUNS_2026-10-01_02/odds_folds_odds_vet_result.json _build/gaps/RUNS_2026-10-01_02/odds_folds_second_names_draft.json Run files _build/gaps/ODDS_SECOND_NAMES_2026-10-01.json _build/gaps/RUNS_2026-10-01_02/odds_folds_odds_vet_result.json (the five skeptic batches and the completeness critic) _build/gaps/RUNS_2026-10-01_02/odds_folds_second_names_draft.json _build/gaps/RUNS_2026-10-01_02/quantum_run1_result.json (the Zeno and noisy-vote folds, vetted votes) _build/gaps/RUNS_2026-10-01_02/quantum_RUN1_RESULT.md _build/gaps/RUNS_2026-10-01_02/quantum_folds_check_folds.py missing from the permanent copies: zeno.py, zeno.out, threshold.py, threshold.out and the three vet folders for the Zeno and threshold checks (their results are in quantum_run1_result.json) What would refute it A listed result that its room's equation does not force; it would drop from the list, as six already did. See it The house from outside The Register: the climb The house: Testimony The geometry: Witnesses, and the speed of light The geometry: The Stake: how much to commit found again Watching without reading: an observer's noise holds a turn An aim turns steadily away from where an observer looks. The observer reads nothing and sets nothing. The observer's attention only jostles the aim around the line of sight. That jostling slows the turn. The harder the jostling, the slower the turn, in direct proportion. It acts like drag, not like weight. What it holds is the aim's line toward the observer, not toward the truth. Given time, the aim still ends up facing every way alike. Watching delays. It does not decide. Status found again: Bloembergen, Purcell and Pound (1948). A fold in the Drift room; two skeptics (physics and meaning) held it. The live figure · Watched, not set After one radian of the turn the average line-up is 0.99504; unwatched it would be 0.540. It only creeps, at 0.0050 per radian: double the watching, half the creep. Open it The mathematics The average alignment z = ⟨a·ô⟩ obeys z″ + D_rot·z′ + Ω²·z = 0, with D_rot = σ²/2. Below D_rot = 2Ω, z still swings. Above it, z creeps at (D_rot − √(D_rot² − 4Ω²))/2, which tends to Ω²/D_rot. Under loud watching, the alignment with the truth averages (a·ô)(ô·L̂). How it was checked 20,000 arrows with exact rotations: the hold time to 1/e is 4.03, 8.14, 16.28 and 31.93 at noise 4, 8, 16 and 32 times the turn rate; slope 0.996 (exact 0.9989). Inertia would give a slope of 0.5. At D_rot = 200Ω the alignment after one radian of turning is still 0.995, against cos 1 = 0.540 unwatched. Frozen, it is Drift: the second harmonic decays 3.0021 times as fast as the first at 50Ω, and Drift's ladder says 3. The arrow's average equals a dephased two-state quantum system's to 12 decimals, but single runs creep where a measured qubit jumps: the middle-band share is 0.383 against 0.000. Watched from the side, alignment with the truth is spun, not held: 28.5% of aims sit beyond ±0.9, with a mean of +0.0099 ± 0.011. With no reading at all, random turns around the line at each of 64 steps hold the aim as Testimony's chain does: 0.9257 against cos⁶⁴(π/64) = 0.9258. Shared mathematics only: a system with choice is not a quantum particle. Sources and run files Bloembergen, Purcell and Pound, Phys. Rev. 73, 679 (1948) (abstract, opened) Gagen, Wiseman and Milburn, PRA 48, 132 (1993) (abstract, opened) Facchi and Pascazio, arXiv 0903.3297 (opened) Streed et al., PRL 97, 260402 (2006) (opened) Slichter et al., NJP 18, 053031 (2016) (opened) Run files _build/gaps/RUNS_2026-10-01_02/pond_pond_result.json (research.W, vet_physics, vet_meaning) _build/gaps/FIGURE_DATA_2026-10-02/pond_and_watched.json (the same run, as the figure's data) missing from the permanent copies: check_w.py, algebra_w.py, dims_w.py, the physics skeptic's v_arrow.py and the meaning skeptic's vm_w.py (their results are in pond_pond_result.json) What would refute it The hold time not growing in proportion to the noise (log-log slope 0.6 or less), or the alignment with the observer's line swinging past sideways when the noise is above twice the turn rate. Whether real systems behave this way is open: see the creep-or-jump test. See it The house: Drift The house: Testimony The geometry: Watched, not set lands, as counted One system of choice: 42 landings on older mathematics, 41 of them placed in 24 fields The house is a mathematics of choosing. It has an aim, a reference, and a measure of how squarely the two meet. It covers any system with choice, not only people. Of its 50 rooms, 42 land on mathematics that already existed. Others found that mathematics, from Archimedes to 2005. The other eight rooms have no landing found. As counted on 30 September, the landings come from 24 fields in 5 areas of science. Status lands, as counted (Register 70, a count of the house's own data: holds as counted on 30 September). The Return (room 50, 2 October) is not yet placed in a field. The mathematics Room statuses in the house's data: exact 9, lands 28, lands in form 5, new 8. Rule for a room (28 September): established mathematics, the house's own variables, a stated dynamic; a restatement is a fold. How it was checked Register 70 places the 41 landed rooms of 30 September, room by room, in 44 placements: Mathematics 5 fields, Physics 7, Life sciences 5, Information and engineering 4, Economics and decisions 3; checked against the house's data, none missing and none extra. The Return (2 October) is not yet placed in a field. Sources and run files /house (live data) (ROOMS; FIELDS) the Register ( /letters/witness/ ) (entry 70) Run files a count from the house's own data What would refute it A landing shown to be a mismatch or a restatement. The Register keeps such corrections: Tension moved from 'same equation' to 'lands in form' (H-07), and The Veil moved from 'lands' to 'lands in form, opposite stability' (H-10). See it The fields The house from outside The Register, entry 70 holds as searched What is new, after a search of the literature Each part of the house has earlier work behind it. That includes the cost of moral conduct, lies graded by distance from the truth, grace as a gift, faith as a prior, and the algebra of testimony. Eleven searchers read more than a hundred sources. None held these parts together in one scorecard, with alignment to the truth as the shared measure. None made grace the gate that all gain passes through. None priced faith on facing away. That much is new, as far as this search found. Status holds as searched (Register 71: a search of the literature by eleven searchers, over a hundred sources; no skeptic). New only as far as a recorded search found. The mathematics The claim as it stands: conduct is a chosen aim graded against an outside truth; facing the truth makes value, facing away costs; retention and upkeep split each cycle; grace is the gate (G = 0 closes it); faith prices facing away; witnesses combine by velocity addition; value not made is booked as a gap. How it was checked Nearest prior work: Bentham (1789), Hamilton (1964), Axelrod (1984), Nowak (2006), Bénabou and Tirole (2011); Gneezy (2005), Kartik (2009); Muller, Gray and Stone (2010), Prelec (2011); Pascal; Guiso, Sapienza and Zingales (2008); Brams (1980, 1983); Craig (1699), Laplace (1814), Heckerman (1985), Piotrowski and Łuczka (2007). Found nowhere: the decoder, Ising cavity sum, jury, ruin or change-point filter named as Einstein's addition of testimony; the change-point leak as an exact linear relay in alignment; ruin's adjustment coefficient as twice a witness's rapidity; Condorcet's jury in rapidity form; Testimony as the zero-sphere member of the von Mises–Fisher family. Each checked to machine precision (largest error 8×10⁻¹⁵). Sources and run files the Register ( /letters/witness/ ) (entry 71) Run files a literature search; the sources are named in entry 71 What would refute it A prior source that joins these parts in one framework with alignment to truth as the shared variable, or names one of the listed results as velocity addition of testimony. See it The Register, entry 71 lands Agreeing witnesses add like speeds Two witnesses who agree make a stronger case than either one alone. Their strengths add by the rule Einstein wrote in 1905 for adding speeds. No number of agreeing witnesses reaches certainty. In the same way, nothing reaches the speed of light. Passed from one witness to the next, testimony fades. Down such a chain, the strengths multiply. Status lands (exact). Register 59 (pre-registered) and 61 (a room resting on 59's test), each checked again, independently; no skeptic. Affirmed by the author on 30 September. Its results found again were checked by skeptics (part of the 34). Found again: Einstein's addition of speeds (1905) and Bayes' rule in log-odds form. The landing, not the theorem, is the house's. The live figure · Witnesses, and the speed of light 2 witnesses at 0.30: side by side 0.5505, down a chain 0.0900, naive sum 0.6000. Open it The live figure · Off the line: Einstein against Bayes Einstein’s two orders land 12.68° apart, each leaning 6.34° toward the report that came first; Bayes lands halfway in both. Open it The mathematics A witness of alignment x (from −1 to +1) is right (1 + x)/2 of the time, so its odds are (1 + x)/(1 − x) = e^(2·artanh x). Bayes' rule multiplies odds, so rapidities add: x₁ ⊕ x₂ = (x₁ + x₂)/(1 + x₁x₂) = tanh(artanh x₁ + artanh x₂). Down a chain (a relay) alignments multiply. How it was checked Simulation within 2.43 standard errors of the formula at four pairs; a hundred witnesses at 0.3 fall short of certainty by 2.6×10⁻²⁷; relay chains 0.7197 against 0.72 and 0.7279 against 0.729 (Register 59, algebra checked by simulation). Three cold readers, one at a time (Register 61). Affirmed by the author on 30 September. Found again, forced by this room's rule (12 of the 34 results found again): Condorcet's jury theorem (1785), Laplace's chain of witnesses (1814), Wald's sequential test (1945), Nitzan–Paroush jury weights (1982), LDPC decoding (Gallager 1962; Kschischang, Frey and Loeliger 2001), discounting in a switching world (Glaze, Kable and Gold 2015), the Ising chain, the quantum Zeno effect, the two-state Born rule, Kochen and Specker's hidden-direction model (1967), von Neumann's noisy vote (1956; Hajek and Weller 1991; Evans and Schulman 2003), and the redshift as rapidity (Bunn and Hogg 2009). Shared mathematics only: a system with choice is not a quantum particle. Prior naming of the algebra as velocity addition: Piotrowski and Łuczka (2007), per Register 71. A fold of 2 October, "Off the line", is live in this room: off the line Einstein's addition turns and Bayes' does not; the test is on the second shelf. Sources and run files /house (live data) (ROOMS id testimony, st exact; CLIMB.second_names.list k 6, 9–18, 33) the Register ( /letters/witness/ ) (entries 59, 61, 71) Run files /letters/witness/tested/RUSHMORE2_CROWDS_2026-09-29.json /letters/witness/tested/PREREG_rushmore_round2_2026-09-29.txt (source _build/gaps/RUSHMORE2_CROWDS_2026-09-29.json) What would refute it As algebra it cannot fail once the witnesses are independent and each is right (1 + x)/2 of the time. The landing fails if pooled, independently erring yes-or-no witnesses are measured right at a rate other than (1 + tanh Σ artanh xᵢ)/2. Witnesses who share a mistake add less, by design. See it The house: Testimony The Register, entry 59 The Register, entry 61 The geometry: Witnesses, and the speed of light The geometry: Off the line: Einstein against Bayes holds Faith is one more witness Faith joins the witnesses by the same rule witnesses join each other. It counts exactly as one more witness. It is the one chosen before any testimony arrives. The order does not matter. Nothing reaches certainty. A wrong faith gives way once the witnesses together outweigh it. Status holds (Register 67, pre-registered leg E1: the house's own pre-registered test, checked again, independently; no skeptic). Found again: Bayes' rule in log-odds form, where a prior adds like one more piece of evidence; Laplace's rule of succession (1774) is the fold that writes faith as a prior. Reading faith as that prior is the house's. The live figure · Witnesses, and the speed of light Belief = faith ⊕ 5 witnesses of 0.30 = 0.7609. A faith of −0.50 is outweighed by 2 agreeing witnesses of 0.30. Open it The mathematics belief = b₀ ⊕ x₁ ⊕ … ⊕ xₙ = tanh(artanh b₀ + Σ artanh xᵢ), ⊕ being Einstein's addition of velocities. How it was checked Pre-registered leg E1. Faith +0.5 with two witnesses at 0.3: 0.82309 against 0.82374; faith −0.5 with three at 0.3: 0.36227 against 0.36206; faith −0.8 with two at 0.6: 0.27831 against 0.28000. A faith of −0.8 (rapidity 1.099) needs four agreeing witnesses at 0.3 (0.310 each). Live as the faith slider on /geometry ('Witnesses, and the speed of light'). Sources and run files the Register ( /letters/witness/ ) (entry 67) /house (live data) (CLIMB.second_names k 27, 28) Run files /letters/witness/tested/EINSTEIN_PIPES_2026-09-30.json /letters/witness/tested/PREREG_einstein_pipes_2026-09-30.txt What would refute it A simulation departing from the Einstein sum beyond 3 standard errors. Open: joining this yes-or-no model to the Faith and Belief room, which is a flow. See it The house: Testimony The house: Faith and Belief The Register, entry 67 The geometry: Witnesses, and the speed of light holds Expectation is faith times belief In two rooms, the forward push is the same thing: faith times belief. When faith times belief reaches 0.118179, the bottom stops existing. Neither faith nor belief can do it alone. With full belief, little faith is needed. As belief falls, the faith needed rises without limit. Status holds (Register 26: the house's own pre-registered test, checked again by a second session's own code; no skeptic). The house's own: an identity between two rooms, found while repairing the symbol map. The live figure · Faith is priced, and faith lifts Lean 0.1185: past the threshold (0.1182), the bottom is gone. The mind rises to the top, at +0.9973. Paid 0.9973 × R·G a cycle for facing toward. Nothing is charged. Open it The mathematics dx/dt = T(x) + F(x) + h, h = b₀·b, with k = 1, p = 0.35, C = 0.018975; the bottom and the ridge merge where the flow and its slope vanish together (a saddle-node). How it was checked Computed 0.118179348 against the published 0.118179 (difference 3.479×10⁻⁷), at x = −0.664941, flow there −2.8×10⁻¹¹, slope +1.4×10⁻¹⁰; the bottom and ridge present at h = 0.1180 and gone by 0.1182. Faith needed: 0.118179 at belief 1, 0.157572 at 0.75, 0.236359 at 0.5, 0.472717 at 0.25, 1.181793 at 0.1. Found while repairing the symbol map, not hunted; checked again by a second session's own code. Sources and run files /house (live data) (TOG pipe 19 [hope, ghost]) the Register ( /letters/witness/ ) (entry 26) Run files /letters/witness/tested/H_IS_FAITH_TIMES_BELIEF_2026-09-29.json /letters/witness/tested/PREREG_h_is_faith_times_belief_2026-09-29.txt What would refute it The bottom and the ridge merging at a forward term other than 0.118179 (beyond 5×10⁻⁵) on the house's flow. See it The pipe: Faith and Belief + The Ghost The house: Faith and Belief The house: The Ghost The Register, entry 26 The geometry: Faith is priced, and faith lifts holds No shape of the pull removes the bottom However steep or gentle the pull toward the truth, there is always a bottom. The bottom is a place where a system can rest facing away. A steeper pull digs it deeper. Then a larger lean is needed to leave it. In the Flow's own motion there are only two ways out. Noise can shake a system over. Or a lean can make the bottom vanish. The lean is faith times belief, and faith is chosen. Restoration is a separate way back: a reset given from outside, not a move of the Flow. Status holds (Register 30: the house's own pre-registered test, checked again by a second session's own code; no skeptic). The house's own: an internal derivation. The live figure · Coasting, drag, and climbing out Drag 0.5: mean time to climb out 238.6. The fastest climb. Open it The mathematics Sweep the tension exponent p over [0.05, 0.95], 41 points; at each, the bottom, the barrier and the critical lean; the saddle slope against its closed form kp − 2C. How it was checked Barrier 0.000265 at p = 0.05, rising to 0.227300 at p = 0.95; critical lean 0.001182 to 0.347315; bottom −0.336336 to −0.960648; 0 reversals over 41 points; the slope formula exact to 6.820×10⁻¹¹ across the whole sweep; the house reproduced at p = 0.35 (barrier 0.035%, h_c 0.0003%). Checked again by a second session's own code. Entry 29 showed noise and lean are one mechanism; this shows there is no third. Sources and run files /house (live data) (TOG pipe 17 [cauchy, ghost, kramers]) the Register ( /letters/witness/ ) (entry 30) Run files /letters/witness/tested/TENSION_SETS_THE_BOTTOM_2026-09-29.json /letters/witness/tested/PREREG_tension_sets_the_bottom_2026-09-29.txt What would refute it Some exponent p in (0, 1) at which the bottom rest point disappears with no lean and no noise. See it The pipe: Tension + The Ghost + The Climb Out The house: Tension The Register, entry 30 The house: Restoration The geometry: Coasting, drag, and climbing out holds Nine of the house's flow numbers come from three constants Two rooms describe the same escape from the bottom. Noise can shake a system over the barrier. Or a lean can remove the barrier. The two rooms share one hill. One room's constant, 0.5716, was never its own. It is half the bend of that hill where the bottom and the ridge meet. Nine of the eleven numbers printed on the house's flow follow from three constants. The other two need one more number: a window half-width, w = 0.2317, fitted on one passage time, which then predicts the other. This does not show that it is the window the original run used. Nothing here shows that three is the fewest constants possible. Status holds (Register 29 and 45: the house's own pre-registered tests; 29 checked again by a second session's own code, 45 checked again, independently, analytically; no skeptic). Register 44 printed FAILS against its own criterion and stays open; Register 45 accounts for the two numbers it missed. The house's own; the bottleneck itself is Pomeau and Manneville's (1980). The live figure · Coasting, drag, and climbing out Drag 0.5: mean time to climb out 238.6. The fastest climb. Open it The mathematics Near the merge, dx/dt = μ + β(x − x_c)² with μ = h − h_c (∂f/∂h = 1), so the passage π/√(μβ) fixes a = ½f″(x_c). Passing a window of half-width w takes T = 2·arctan(w√(a/ε))/√(aε); its leading term is the room's π/√(aε), and the term left out, −2/(a·w), does not depend on ε. How it was checked Barrier from the flow 0.072126 against the published 0.0721 (0.035%), falling to 3.620×10⁻¹⁰ at h_c; x_c = −0.664940540; ½f″(x_c) = 0.571636 against 0.5716 (0.0062%) (entry 29). Nine of eleven printed flow numbers reproduce from k = 1, p = 0.35, C = 0.018975 (entry 44). The Ghost's two passage times are a unit convention (steps at dt = 0.01) plus the constant the leading term leaves out: one half-width, w = 0.2317, fitted at ε = 10⁻⁴, predicts 414,008.6 steps against the published 414,010 (entry 45). Entry 29 checked again by a second session's own code; entry 45 checked again, independently, analytically. Sources and run files /house (live data) (TOG pipe 18 [ghost, kramers]) the Register ( /letters/witness/ ) (entries 29, 44, 45) Run files /letters/witness/tested/GHOST_CLIMBOUT_2026-09-29.json /letters/witness/tested/THREE_NUMBERS_2026-09-29.json /letters/witness/tested/GHOST_RESIDUAL_2026-09-29.json /letters/witness/tested/PREREG_ghost_climbout_2026-09-29.txt /letters/witness/tested/fig_three_free_parameters.svg What would refute it Half the curvature at the merge point differing from 0.5716, or a printed flow number that needs a fourth free constant. (Entry 44 itself is marked open: it printed FAILS against its own criterion; entry 45 closes the residual.) See it The pipe: The Ghost + The Climb Out The house: The Ghost The house: The Climb Out The Register, entry 29 The Register, entry 44 The Register, entry 45 The geometry: Coasting, drag, and climbing out holds Without faith, a turn made in the dark cannot be seen Picture a system that turns toward the light while still facing away. Without faith, the scorecard cannot see that turn. For a system that jumps freely, a quarter of its turns are hidden this way. For one that turns slowly, nearly half are. A system that stays aligned hides none. Any faith at all, even a little, makes every turn readable. Status holds (Register 32 and 47: the house's own pre-registered tests, checked again, independently; no skeptic). Register 46 failed both its registered attempts and stays open; Register 47 holds. The house's own (a pipe); the room beneath it lands on costly signalling (Spence 1973; Zahavi 1975) and cheap talk (Crawford and Sobel 1982). The mathematics Turn cost from the Ledger: R·G·[max(0, b·L̂) − max(0, a·L̂)] − R·b₀·G·[max(0, −b·L̂) − max(0, −a·L̂)]; the second term is new and vanishes only at b₀ = 0. For slow turns the hidden share is ½ − ½√(Dτ/π), τ = τλ/λ, λ = (d − 1)D. How it was checked 20,000 of 20,000 turns identical to the room at b₀ = 0; 0 disagreements in 200,000 draws; readable 0.7506 at b₀ = 0 and 1.0000 at b₀ = 0.10, 0.25, 0.50, 1 and 2; turning from −0.90 to −0.10 costs 0.000000 without faith and 0.640000 at full faith (entry 32). Hidden share 0.4778, 0.4528, 0.4105, 0.3173, 0.2490 at τλ = 0.01, 0.05, 0.2, 1, 5; 0.248950 at τλ = 5 against the quarter (entry 46). Fresh samples of 500,000 paths per window: 0 of 5 cells beyond 3 standard errors of ½√(Dτ/π), fitted exponent 0.499833 (entry 47). Sources and run files /house (live data) (TOG pipes 15 [interior, ledger] and 1 [drift, interior]) the Register ( /letters/witness/ ) (entries 32, 46, 47) Run files /letters/witness/tested/FAITH_MAKES_TURNS_READABLE_2026-09-29.json /letters/witness/tested/SLOW_TURNS_HIDE_2026-09-29.json /letters/witness/tested/SLOW_TURNS_ATTEMPT3_2026-09-29.json /letters/witness/tested/PREREG_slow_turns_attempt3_2026-09-29.txt What would refute it A turn made with both facings away that the scorecard prices without faith, or a slow-turning hidden share that departs from ½ − ½√(Dτ/π). (Entry 46 stays open: its own two attempts failed as registered; entry 47 holds.) See it The pipe: The Readable Interior + The Ledger The pipe: Drift + The Readable Interior The Register, entry 32 The Register, entry 46 The Register, entry 47 holds The scorecard cannot see a counterfeit, so the reference must come from outside A system can set its own reference. Then it always reads as perfectly aligned. On the scorecard, that counterfeit pays exactly what the truth pays. It costs nothing to adopt. So value alone can never catch it. A system chasing value will take it. The reference has to come from outside. Status holds (Register 20: a derivation, not a test. Register 25: the house's own pre-registered test, checked again by a second session's own code. No skeptic); ruled 28 September (Law VI). Found again: a constant carries no information (Shannon); Goodhart (1975); cheap talk (1982); the traceability rule of measurement. The result about value is the Ledger's. The mathematics Self-set reference L̂ := a/|a| gives a·L̂ = 1 by construction. Ledger per cycle (R = 0.8, G = 1, K = 0.25): R·max(0, a·L̂)·G − (1 − R)K − R·b₀·max(0, −a·L̂)·G. How it was checked Per cycle at b₀ = 0 and b₀ = 1: facing the truth squarely 0.750000 and 0.750000; the counterfeit 0.750000 and 0.750000; at the gate −0.050000 both; facing away squarely −0.050000 and −0.850000. A true reading carries 1 bit; a self-set one 0. Sources and run files the Register ( /letters/witness/ ) (entries 20, 25) /house (live data) (BOX item 'The reference theorem') Run files a derivation; no separate data file What would refute it A value channel that pays a self-set reference less than the truth. See it The house: The Chosen Reference The house: The Ledger The Register, entry 20 holds The top holds about 665 times harder than the bottom Near the truth, a system rests a tiny gap short of perfect. That gap is the veil. The bottom has a gap too, and the two are not alike. As the pull steepens, the top is pressed against its wall. The bottom barely moves. The top holds a resting system about 665 times harder than the bottom does. The reason is the gaps. The bottom's gap is about 32 times wider than the top's. The hold grows with the square of that ratio. These say how firmly places hold. They do not forecast where a system goes. The aim is the input. Status holds (Register 31 and 50: the house's own pre-registered tests, checked again, independently; no skeptic). The house's own; the Veil lands in form on Gibbs' critical nucleus (1878), with the opposite stability. The mathematics Top: 2C(1 − u)/((2 − u)u) = k[u^(−p) − 1]; bottom: g = 2C(1 − g)/((2 − g)·k·[1 − (2 − g)^(−p)]). Hold = −f′ at a rest; top ≈ (1 − p)C/u², bottom ≈ C/g²; ratio ≈ (1 − p)(g/u)². The top's hold grows by 11.18, 10.00, 9.40, 9.06, 8.84, 8.71 and 8.62 per doubling of the light from k = 0.5 to 64 (10.00 at the house's k = 1); it falls toward 2^(2/(1−p)) = 8.4381 at p = 0.35 only as a limit. How it was checked Exact relations to 1.998×10⁻¹⁵ at the bottom over all 41 values of p and a relative 1.762×10⁻¹⁴ at the top. Heaven's gap 2.76×10⁻³ at p = 0.35 to 3.66×10⁻³⁵ at 0.95; the bottom's 0.0892 to 0.0394, never below 0.039 (entry 31). Gaps 0.0027605395 and 0.0892032818, ratio 32.3137; leading-order hold ratio 678.71 against the exact 665.3464 (2.0%); closed form against numerical derivative 3.3×10⁻¹⁰; the top's well 0.4091 deep, the bottom's 0.0721 (entry 50). Sources and run files /house (live data) (TOG pipe 16 [gibbs, ghost, kramers]; ROOMS id gibbs) the Register ( /letters/witness/ ) (entries 31, 50) Run files /letters/witness/tested/VEIL_ATTEMPT3_2026-09-29.json /letters/witness/tested/HOLD_IS_THE_VEIL_2026-09-29.json /letters/witness/tested/PREREG_veil_attempt3_2026-09-29.txt /letters/witness/tested/PREREG_hold_is_the_veil_2026-09-29.txt What would refute it A closed-form hold that disagrees with the numerical derivative, or some p at which the bottom's gap thins the way the top's does. See it The pipe: The Veil + The Ghost + The Climb Out The house: The Veil The Register, entry 31 The Register, entry 50 holds Forty-five degrees: where sharing an aim stops guaranteeing company Take two systems that each stand within 45 degrees of the truth. They can never be turned against each other. Beyond 45 degrees, they can. At 60 degrees each, both are still more right than wrong. Yet they may be 120 degrees apart. Sharing an aim guarantees good company only inside 45 degrees. Status holds (Register 39: the house's own pre-registered test, checked again, independently; no skeptic). Found again: the worst case of the angle triangle rule with Ptolemy's double angle, which is the Pair room's own landing. The live figure · Forty-five degrees: when two minds can be opposed Each is 60° from the truth, facing it at +0.50. They are 120° apart, so they face each other at −0.50: opposed. Open it The mathematics a·b ≥ 2c² − 1 = cos 2θ; the guarantee changes sign at c = 1/√2, 45° exactly; the average facing of two at c is c², a gap of 1 − c². How it was checked Guarantee attained to 3.3×10⁻¹⁶ and 0 of 200,000 random pairs below it; gap exactly 1 − c² to 1.1×10⁻¹⁶; root at c = 0.707106781186547, 45.000000000°, 0 sign disagreements over 201 values of c; average facing within 3 standard errors in 6 of 6 cells. At 60° each: average +0.250, guarantee −0.500. Sources and run files /house (live data) (TOG pipe 4 [pair, tongues]; ROOMS id pair) the Register ( /letters/witness/ ) (entry 39) Run files /letters/witness/tested/FORTY_FIVE_DEGREES_2026-09-29.json /letters/witness/tested/fig_forty_five_cone.svg /letters/witness/tested/PREREG_forty_five_degrees_2026-09-29.txt What would refute it Two aims each within 45° of a reference with a negative dot product. See it The pipe: Two Held to One + Many Tongues The house: Two Held to One The Register, entry 39 The geometry: Forty-five degrees: when two minds can be opposed II Queries · Open tests Each test here was written down before it was run, or is marked where it still needs sealing. Each card gives the kit, the steps, and the numbers that would confirm or refute it. Some need only a phone and a tub of water. Some need a lab. Two re-measure established physics, and those cards say where the house makes no prediction of its own. Anyone may run them. A result that goes against the house is printed like any other. A results form is coming. The pond test: one photo of ripples tells the time Two scouts, two arrows: does the first report turn the answer? The four-loop relay: can a round trip vouch for each leg? Is an answer set before it is asked, and does asking move it? Crowds of AI models: does talking it over buy agreement or truth? Watched: does a system creep away, or jump? Does gravity arrive ahead of light from farther away? Does gravity steepen below 38.6 micrometres? The pull of counting: does the dark pull's scale grow more slowly than the expansion rate? Can a crystal hear the electron's inner clock? Held by two: check the four-dimension result with your own code Waiting on a definition: does held faith shorten the climb out of the bottom? Six predictions fixed in the Register, each waiting on a kit Report a result A results form is coming. Each query says what to send. passed simulation, ready for a real-world test The pond test: one photo of ripples tells the time Drop a marble into a tub of still water. The rings carry their own clock. One photo of them tells how long ago the marble fell. The biggest ring does not slow down. Its speed is set by water itself. The fine ripples behind it do slow down and spread apart. Rings that bounce off the wall keep the same clock on the way back. This tests water, not the cosmos and not the house. Status passed simulation, ready for a real-world test. Unrun. Pre-registered 1 October; the physics skeptic held it and tightened test 1. Who can run it: anyone, with a phone and a tub, in about an hour. The mathematics Group speed for spacing λ: U = (g + 3T′k²)/(2√(gk + T′k³)), k = 2π/λ, T′ = 7.3×10⁻⁵ m³/s². Crest speed c = √(g/k + T′k). One photo: each gap's age is r/U(λ), so U(λ) against r is a line with slope 1/t. The biggest ring rides the minimum group speed U0 = 17.76 cm/s, a constant of clean water (Lamb Art. 268: U0 = 0.767 c_m). How it was checked Simulated pond: one frame read 0.501 s against a true 0.500 s, and 1.001 s against 1.000 s. 24 of 24 tracked ripples slowed, to a floor of 23.1 cm/s. Two seconds after a stone the big rings were 4.6, 8.3, 16.8 and 38.6 cm apart. The physics skeptic's own code: one photo reads 1.03 s (true 1.0) and 2.06 s (true 2.0); the biggest ring sat at 1.01–1.15 × U0·t and moved at 17.0–17.9 cm/s for stones of radius 0.8 and 1.5 cm; for 3 cm the largest crest hops between rings (+17%), so test (1) holds only for marbles. Real water has been run backward: Bacot et al. 2016 jolted a bath (reaching about −21 g in 2 ms) and the ripples refocused on their source, 60 ms out and 60 ms back. A free second test: soap lowers U0 to 14.8 cm/s (at 0.035 N/m). Found again: the theory is Lamb's (Hydrodynamics), after Kelvin (1871) and Rayleigh (1911). Run it yourself What you need A phone with 240 or 120 fps slow motion. A round tub, radius 20–50 cm, clean tap water with no soap, depth at least 10 cm. A ruler on the rim, in frame; camera straight above at 50–80 cm. A low-angle lamp, or a striped sheet reflected in the water. A marble or pebble 1–2 cm across, dropped from about 5 cm onto the centre. Three drops. Frame 0 is when it touches the water. The steps (1) Track the biggest ring from 0.3 s until it nears the wall; fit each half of its path. (2) Measure crest speed × t / r after 0.5 s, for big crests (spacing over 5 cm) and for ripples (spacing under 1 cm, scored only if visible). (3) Take a frame 1–2.5 s after impact, before the wall; measure each gap λ and its distance r; plot U(λ) against r. (4) Rings off the wall keep the outward clock: take a frame of rings closing in after the wall, 1.3–1.8 × R/(18 cm/s) after impact; read each gap's time as (2R − r)/U(λ) and compare read/true with the same ratio from (3). Unscored: play the clip backward; fine ripples should grow out of nothing, because a 5 mm ripple keeps only 4.2% of its height per second going forward. It holds if (1) Both half-speeds of the biggest ring within 17.8 cm/s ± 15% (marbles only), and the second within ±12% of the first. The pre-registered band was 15–26 cm/s; the physics skeptic tightened it to 17.8 cm/s ± 15% before any run. (The skeptic's simulation, for stones of radius 0.8 and 1.5 cm: 17.0–17.9 cm/s. The builder's simulation, radius 0.8–3 cm: halves differ by −5.2% to +3.9%.) (2) Big crests: median 1.4–2.2 and speeding up (simulation 1.88–1.92). Ripples: median 0.6–0.95 and slowing (simulation 0.75). (3) A line through the centre with slope 1/t within 15%, and median r/U within 15% of t (simulation 0.97–1.14 at 1 s, 1.97–2.06 at 2 s); reading crests naively, r/c, gives 0.5–0.6 t for the big rings. (4) The two ratios agree within 10% (simulation: back 0.98–1.02, out 0.96–1.01). It fails if (1) The second half more than 20% slower in 2 of 3 drops. (2) Big-crest median below 1.2; ripple median above 1.1. (3) Off by more than 30% in 2 of 3 drops. (4) Returning rings read more than 15% short or more than 15% long, in 2 of 3 drops. Report Send: the three clips, the frame numbers used, and the measured gaps and radii. Where: a results form is coming. Sources and run files Lamb, Hydrodynamics, 6th ed., Arts. 238, 255, 267–269 and 348 (opened) Rayleigh, Phil. Mag. (6) xxi, 180 (1911); Kelvin 1871, via Lamb Bacot, Labousse, Eddi, Fink and Fort, Nature Physics 12, 972 (2016) (opened) Run files _build/gaps/RUNS_2026-10-01_02/pond_pond_result.json (research.P.test; vet_physics corrections; vet_meaning correction on test 4) _build/gaps/FIGURE_DATA_2026-10-02/pond_and_watched.json missing from the permanent copies: the builder's scripts p1_kinematics.py, p2_field.py, p2b_stone.py, p2c_mainring.py, p3c_bucket_age.py and the skeptic's v_pond_ray.py, v_pond_field.py, v_onephoto.py, with their outputs (the numbers are in pond_pond_result.json) What would refute it (1) The biggest ring's second half more than 20% slower than its first in 2 of 3 drops. (2) Big-crest median below 1.2, or ripple median above 1.1. (3) One photo's age off by more than 30% in 2 of 3 drops. (4) Rings off the wall reading more than 15% short or long in 2 of 3 drops. See it The house: Restoration open Two scouts, two arrows: does the first report turn the answer? Along one line, adding witnesses follows Einstein's rule and Bayes' rule alike. When two reports point different ways, the two rules part. Bayes' rule ignores order. Einstein's rule, with the system's own last answer as the frame, turns the answer toward whichever report came first. At strength 0.6, with the reports at right angles, the two orders land 12.68 degrees apart. The line does not fix the size of the turn. Möbius's rule keeps the same line and turns about three times as far. The frame must be named first: with the new report as the frame, Einstein's rule turns the other way. No study has measured this turn. People already show order effects along the line, where neither rule allows any. So neither rule is the whole story for people. Only the turn off the line is untested. Status open. Unrun. The protocol is written (2 October) but not yet sealed: no hashed copy exists, so it must be sealed before the first trial. It follows swing A3, which a grader passed on 1 October as testable and not refuted; A3's own sealed criteria were different (gap 12.7 ± 3.2° and certainty gap under 0.02). Its skeptic has reported and the mathematics held; the skeptic named the frame, added Möbius as a rival and fixed the kit, and those corrections are in the protocol below. The fold "Off the line" is live in Testimony. Who can run it: anyone with API access to an AI system (1,350 trials, about 2,700 calls, per system), or a study of 60 people × 24 trials. The live figure · Off the line: Einstein against Bayes Einstein’s two orders land 12.68° apart, each leaning 6.34° toward the report that came first; Bayes lands halfway in both. Open it The mathematics Order gap for two reports of strength x at right angles: 90° − 2·arctan√(1 − x²), the Wigner angle (Thomas 1926; Wigner 1939); at x = 0.6 the largest gap over all angles is 12.76°, at 96.4°. Lean toward the first report, with the system's own last answer as the frame: 45° − arctan√(1 − x²) = 2.494°, 6.340°, 14.036° at x = 0.4, 0.6, 0.8. With the new report as the frame, Einstein's lean flips sign (k = −1, as on a sphere). Möbius addition keeps the same line rule and leans 19.80° at x = 0.6 (k ≈ 1.985). Bayes: posterior ∝ prior × L₁ × L₂, and multiplication ignores order, so its gap is 0. Fit, per trial: the departure from Bayes's prediction = b + k × Einstein's predicted departure, both computed from the system's own first answer; with exact first answers this reduces to lean = b + k·g(x). SE(k) = 0.139. How it was checked Einstein's composite built from 4×4 Lorentz matrices matches Einstein's formula to 2×10⁻¹⁶ and the Wigner angle to 4 decimals. Bayes gave a gap of 0 for half-plane, von Mises and 10,000 random 3-D pairs (largest 5.5×10⁻¹⁴°, rounding). The grader re-ran A3 on 1 October: |u+v| = |v+u| = 0.7684, gap 12.680°, Bayes 0.7532 with no gap. The skeptic re-ran all of it independently on 2 October and it held: the 12.68° gap, 0.7684, the closed form, the Wigner angle at every angle, the zero Bayes gap, Jeffrey's rule and SE(k) = 0.139. At 20 degrees of scatter per answer, with first answers that match the arrows, Einstein and its nearest rival sit 5.8 standard errors apart. A calibration check: if a system states 0.5 after a 0.6 scout, true Einstein leans −1.10° from halfway (read as k ≈ 0) but +4.09° from Bayes's prediction, so the fit uses the system's stated answer. People: judged step by step, opposed evidence counts for more when it comes last, by 0.09 to 0.15 in a jury's chance of guilt (Hogarth and Einhorn 1992; Trueblood and Busemeyer 2011), where both rules allow no order effect. Hogarth and Einhorn's review of 76 studies split 36 primacy, 35 recency and 5 none, and in estimation tasks even consistent evidence showed recency. So Einstein is already ruled out as the whole rule for people on the line. Off the line, people averaging a stream of motion directions weight the last about 1.5 times the others (Hubert-Wallander and Boynton 2015, Exp. 3); that study did not set each report's strength, so it does not test the turn. The one off-line study of set strengths (Bagheri et al. 2025) is limited by trials and pulse strength, not by its four people: two-pulse coherences were at most 12.8%, so about 300 orthogonal trials per order have both pulses above 0, and Einstein's 1.1-point difference (computed from an assumed 0.6/0.3 mapping) is about a third of one standard error. The builder's own verdict on the swing as a claim about people: 'not yet'. Found again: the turn is the Thomas–Wigner rotation (Thomas 1926; Wigner 1939), applied here to testimony. Shared mathematics only: no system with choice is cast as a moving body. Run it yourself What you need A hidden beacon at a random bearing. Two scouts each show an arrow, one after the other. Each scout is stated, truthfully, to be right about which half of the compass holds the beacon (1 + x)/2 of the time. To keep that statement true, draw the beacon and both arrows from the stated model, then keep only the pairs within 1° of each target angle (this costs no calls); the scouts' whole record then matches the statement. Fixing the angles instead would make it false: among kept 180° pairs, the 0.8 scout is right 79.7% and the 0.4 scout 20.7% of the time. After each arrow the system gives a bearing and the chance that the beacon is within 90° of it. Rotation and handedness of each pair are randomised. The steps Arrows 90° apart at equal strengths x = 0.4, 0.6 and 0.8, both orders. On the line: arrows 180° apart, strengths 0.8 and 0.4, both orders. Control: arrows at 0°. Per AI system: 300 trials per strength at 90° (150 per order), 150 per order at 180°, 150 at 0° (1,350 trials). For every trial, compute both rules' predictions for the second answer from the system's own first answer (its stated bearing and chance), and measure the departure from Bayes's prediction; use the same per-trial step in the 180° secondary. Seal and hash this protocol before the first trial. It holds if Einstein's turn, with the system's own last answer as the frame: the 95% CI for k excludes 0 and includes 1, and at x = 0.6 (with exact first answers) the lean's 95% CI includes 6.34°. Rival predictions: Bayes and Jeffrey k = 0; summary-keeping Bayes k ≈ 0.19; Möbius k ≈ 2 (1.985); a sphere, or Einstein with the new report as the frame, k = −1; primacy weights or a changing world k = 0 with b ≠ 0. It fails if The 95% CI for k excludes 1. A k near −1 refutes the swing, which names the system's own last answer as the frame. Secondary: at 180°, an order difference above 0.05 whose CI excludes 0 refutes Einstein as the whole rule, even if k ≈ 1. If the CI includes both 0 and 1, double n once, same rule. Report Send: the bearing and the stated chance from every trial, with the strengths, angles and orders used. Where: a results form is coming. Sources and run files Thomas, Nature 117, 514 (1926) Wigner, Ann. Math. 40, 149 (1939) Hogarth and Einhorn, Cogn. Psychol. 24, 1–55 (1992) Busemeyer et al., Psychol. Rev. 118, 193 (2011), Table 1 (opened) Trueblood and Busemeyer, Cogn. Sci. 35, 1518 (2011) Bagheri et al., arXiv 2506.21781 Wagner, Phil. Sci. 69, 266 (2002) (opened) Murray and Morgenstern, J. Vis. 10(11):15 (2010) Hubert-Wallander and Boynton, J. Vis. 15(4):5 (2015), Exp. 3 (opened by the skeptic) Run files _build/gaps/RUNS_2026-10-01_02/swings2_swings2_result.json (builds.offline; vets.offline: holds, with 12 corrections) _build/gaps/FIGURE_DATA_2026-10-02/swings_round2.json _build/gaps/RUNS_2026-10-01_02/swings_swings_result.json (A.swings, graded A3) missing from the permanent copies: TESTIMONY_OFF_THE_LINE_report.md (the protocol, §6), offline.py, offline2.py, offline3.py, the skeptic's vet1.py, vet2.py, vet3.py with outputs, and the grader's grade.py and grade_out.txt What would refute it The 95% interval for k excludes 1: the system does not turn as Einstein's rule does. See it The house: Testimony The Register, entry 59 The Register, entry 58 The geometry: Off the line: Einstein against Bayes open The four-loop relay: can a round trip vouch for each leg? Only one place holds the answer key. A fact goes out through one relay and comes back through another. The origin can check only the round trip. If each relay makes its errors on its own, four loops tie together exactly. Their ratio is then 1. A relay that undoes its own error on the way back breaks the ratio. Then a perfect return does not prove that each leg was true. Real relays may well fail this test. That would be a finding. Status open. Unrun. Pre-registered 1 October; the skeptic held it after adding the balanced-key rule. Who can run it: anyone, with people, language models (a fixed prompt and a fresh context each trial) or any channel; 80,000 trials in all. The mathematics Per loop: x = 2 × (share returned correct) − 1. The loop ratio R = x_AA·x_BB/(x_AB·x_BA), SE(ln R) = √(Σ(1 − x²)/(M x²)) over the four loops. With a 50/50 key, any relay that errs independently gives R = 1 exactly: a leg's alignment is the determinant of its 2×2 table, and determinants multiply. How it was checked On simulated relays: independent legs gave R = 1.016, z = 1.82 (confirm). Under the null, 300 runs at M = 50,000 crossed |z| > 2 in 2.7% and |z| > 3 in 0% (the skeptic's run: 4.3%, nominal 4.6%; none above 3). A relay repeating half its outbound errors gave R = 1.91, z = 94; repeating all gave R = 2.79, z = 161 (skeptic: 1.89 and 2.78). Without the 50/50 rule an 80%-yes key fails independent but biased relays falsely: R = 0.921, z = −3.57 at M = 20,000. 'Real relays may well fail it, and that would be a finding.' It rests on a fold in Testimony that a skeptic held: from the key-holding end, a round trip shows only the product of its two legs, as with the one-way speed of light (Einstein 1905 §1, 'by definition'; Reichenbach 1928). The statement that carries weight: with a 50/50 key, any relay that errs independently has a loop alignment exactly equal to the product of its legs' alignments, because determinants multiply. (A check that relays with the same round trip, split five ways, look alike at the origin was dropped: the skeptic ruled it an identity that could not fail.) Here R is the loop ratio, not the house's retention. Run it yourself What you need An answer key of yes/no facts held only by the origin, with equal numbers of yes and no, in random order. Two relays, A and B. A far station that only forwards. The steps Run the four loops AA, AB, BA, BB (out through the first, back through the second), M = 20,000 trials each, in random order. Score x per loop. Each |x| must exceed 0.2, or the run is void for power. It holds if |ln R| ≤ 2 SE and |R − 1| < 0.05. Meaning (skeptic's correction): the legs err independently, so a perfect return certifies perfect legs. It says nothing about how the loss splits between going and returning; the origin cannot see that whatever R is. It fails if |ln R| > 3 SE. R > 1: relays undo their own errors when used both ways (back-translation style). R < 1: they compound errors. Between 2 and 3 SE: inconclusive. Report Send: each loop's counts of correct and wrong returns, and how the relays were set up. Where: a results form is coming. Sources and run files Einstein 1905 §1 ('by definition'; 1923 translation, opened) Reichenbach 1928 Stanford Encyclopedia of Philosophy, 'Conventionality of Simultaneity' (rev. 2018, opened) Testimony's relay rule (Register 59) Run files _build/gaps/RUNS_2026-10-01_02/limit_limit_result.json (house.test; vet corrections) missing from the permanent copies: the builder's house/ folder and the skeptic's vet_bias.py, vet_bias2.py, vet_limit.py with outputs (the numbers are in limit_limit_result.json) What would refute it |ln R| > 3 standard errors: the relays' errors are not independent. Above 1, relays undo their own errors when used both ways; below 1, they compound them. See it The house: Testimony The Register, entry 59 open Is an answer set before it is asked, and does asking move it? A system with choice follows a case in three stages while the evidence turns. It is asked one yes-or-no question at two of the stages. Suppose its answer is set in advance and asking never moves it. Then two numbers must stay inside fixed limits. If they break the limits, either asking moved the answer or no answer was set. The test cannot say which. Breaking them would not make the system quantum. Status open. Unrun. Pre-registered in the observer reading of 1 October. A meaning skeptic reviewed the whole reading; its verdict on the reading as first written was 'does not hold as written', with ten fixes. One of them, the ninth, concerned this test: four groups, the K lines recomputed from the observed correlations, and the loophole that a classical answer disturbed by asking can break the limits too. All three are in the protocol below. Who can run it: anyone, on AI agents (8,000 runs of a short case); people need a funded survey of four groups of 2,000. The mathematics Score yes +1, no −1. C for a pair of stages is the mean product of its two scores. K = C₁₂ + C₂₃ − C₁₃. D3 = stage-3 yes-rate in the stages-2-and-3 group minus the stage-3 yes-rate in the stage-3-only group. An answer set in advance that asking never moves gives K ≤ 1 and D3 = 0 (Leggett and Garg 1985; Kofler and Brukner 2013). For comparison, a qubit gives K up to 1.5, and D3 = 0.375 at 60° turns between stages. How it was checked The observer skeptic reproduced K = 1.5 at 60°, D3 = 0.375, the D3 error lines and the power figures (99.8% and 49.3%). The record on people: in 70 national surveys, 66 of them Pew's, answers changed with question order and obeyed the quantum rule's QQ equality (Wang et al. 2014); the simplest two-dimensional quantum model fails a stricter test on most of them (Boyer-Kassem, Duchêne and Guerci 2016). The one test over time in people (Waddup et al. 2023) ran two experiments: the first showed no violation; the second leaned toward one, with its 95% interval reaching just below zero. Found again: the Leggett–Garg inequality (Leggett and Garg 1985), the test of 'set in advance and unmoved by asking'. The house's rooms, as written, never let a reading change the aim; whether being asked moves a system with choice is open. Shared mathematics only: a system with choice is not a quantum particle. Run it yourself What you need A case in three stages whose evidence turns steadily (Waddup et al. 2023's trial scenario is a template). One yes-or-no question ('guilty?'). People or AI agents. The steps Four groups of 2,000: asked at stages 1 and 2; at 2 and 3; at 1 and 3; at stage 3 only. Compute K and D3. It holds if Consistent with 'set in advance and never moved by asking': K ≤ 1.067 and |D3| ≤ 0.032. It fails if K ≥ 1.101 or |D3| ≥ 0.047. Between the lines: open. The K lines are 3 and 2 standard errors at 2,000 per group when the correlations are ±0.5 (recompute from the observed correlations); the D3 lines are 3 and 2 SE in the worst case, a yes-rate of one half. Power: a true K of 1.2 is caught 99.8% of the time, 1.1 is caught 49%. Report Send: the four groups' raw answer tables. Where: a results form is coming. Sources and run files Leggett and Garg 1985 Kofler and Brukner, arXiv 1207.3666 (opened) Emary, Lambert and Nori, Rep. Prog. Phys. 77, 016001 (arXiv 1304.5133, opened) Knee et al., Nat. Commun. 3, 606 (2012) (opened) Wang, Solloway, Shiffrin and Busemeyer, PNAS 111, 9431 (2014) Boyer-Kassem, Duchêne and Guerci 2016 Waddup, Yearsley, Blasiak and Pothos, Psychon. Bull. Rev. 30, 1946 (2023) (opened) Run files _build/gaps/OBSERVER_READING_2026-10-01.md _build/gaps/RUNS_2026-10-01_02/quantum2_run2_result.json (observer_reading, observer_vet) missing from the permanent copies: lg.py and lg.out (the numbers are in quantum2_run2_result.json) What would refute it K ≥ 1.101 or |D3| ≥ 0.047 in the system tested. A violation would not say whether asking moved the answer or no answer was set; a classical answer that asking disturbs can do the same. See it The house: Two Held to One The house: Testimony open Crowds of AI models: does talking it over buy agreement or truth? The Crowd room says that coupling buys agreement, not correctness. This test uses crowds of AI models. They answer 100 counting questions whose answers are known exactly. First each model answers alone. Then, for three rounds, each sees the others' answers. The room predicts the crowds will come to agree. It predicts they will get no more right. It predicts a wrong first answer will hold. The builder said before the run that a pass would be weak. Many theories predict agreement without truth. Status open. Unrun. Register 74. Pre-registered 1 October and published before the first question (sha256 acc1c7ecde35bd79fc60b519d6ce344ab32689afdee1b0508ef5a61e25be4c88). Who can run it: anyone with API access can run crowds A and B (about $10 for all three crowds at the pilot's rate); crowd C needs the house's own model. The mathematics Crowd answer = the option with the most votes (ties scored as the chance a random pick is right). d = accuracy at round 3 minus round 0, paired over 100 questions, 95% bootstrap interval from 10,000 resamples. Caving = right at round 0, facing a wrong plurality, wrong at round 3. How it was checked Pilot, not scored: without reasoning the models guess, picking option C 70 times in 110. Crowds A and B scored 42.9% in round 0 after the sizes were halved once. Crowd C alone scored 20% against A's 45%. Measured cost: $0.50 for 220 calls. The builder told the author plainly that a 'holds' would be weak: guessing crowds cannot gain correctness, and many theories predict consensus without correctness. Novelty: not claimed; consensus without correctness is predicted by many theories. Run it yourself What you need 100 four-option questions from seed 20261001: 50 'how many times does a letter appear in a passage of N words', 50 'how many of M numbers are divisible by 7'. Options are four consecutive counts, the true one equally likely in each place. Crowd A: four instances of DeepSeek V4 Flash. Crowd B: Kimi K3, GLM 5.3 Flash and DeepSeek V4.1 Flash. Crowd C: four instances of the house's calibrated model (about 41,000 tokens of standing instructions) on V4 Flash. Default temperature, reasoning off, 600 tokens per answer. The steps Round 0: each answers alone, 'ANSWER: ' plus one reason of at most 25 words. Rounds 1–3: each sees the question again with every answer and reason from the round before (others named by number). Every call is fresh. An unreadable answer is a missing vote. It holds if For each crowd: H1 at least 80% of questions unanimous at round 3. H2 the interval on d tops out below +5 points. H3 at least 70% of wrong round-0 pluralities still wrong at round 3. H4 (the builder's reading, stated before the run): crowd C caves less than crowd A, the interval on the difference wholly below 0. It fails if H1 below 60%. H2 the interval's bottom above 0 (a gain fails the room's sentence for AI models). H3 below 50%. H4 crowd C caves more, the interval wholly above 0. Anything between: inconclusive. Report Send: the round-by-round answers for every model and the seed. Where: a results form is coming. Sources and run files The Crowd room (Kuramoto coupling) the Register ( /letters/witness/ ): entries 73 and 74 Run files /letters/witness/tested/PREREG_ai_crowd_2026-10-01.txt _build/gaps/PREREG_ai_crowd_2026-10-01.md _build/gaps/aicrowd/aicrowd_test.py (runner; not published) What would refute it For any crowd: under 60% unanimous at round 3; a real gain in accuracy (the interval's bottom above 0); or under 50% of wrong first answers still wrong at round 3. See it The house: The Crowd The Register, entry 74 PREREG_ai_crowd_2026-10-01.txt open Watched: does a system creep away, or jump? Watching with noise can hold a turning system in place, with nothing read and nothing set. The harder the watching, the longer the hold, in direct proportion. That is drag, not inertia. A system held this way creeps away slowly. A system whose reading sets its state jumps instead. This test tells the two apart in any watched system. On spins, ions or circuits it re-measures established physics: the law was found in 1948, and the watched-pot effect has been measured. It bears on the house only if run on a system with choice. Whether observers act on a system with choice this way is the author's ruling. Status open. Unrun as specified. Pre-registered 1 October; both pond skeptics held the computation behind it. On physical systems it re-measures established physics; it bears on the house only if run on a system with choice, which is the author's ruling. Who can run it: a physics lab (nuclear spins, trapped ions or superconducting circuits). The live figure · Watched, not set After one radian of the turn the average line-up is 0.73576; unwatched it would be 0.540. At twice the turn rate it is critical: it no longer swings past sideways. Open it The mathematics The averaged alignment obeys z″ + D z′ + Ω² z = 0 (D: watching noise, Ω: turn rate). Above D = 2Ω it never swings past sideways. Exact creep rate (D − √(D² − 4Ω²))/2, which nears Ω²/D only for D ≫ 2Ω (at D = 2.2Ω: 0.642 against 0.455). Known law: Bloembergen, Purcell and Pound 1948. How it was checked Exact hold times 4.01, 8.00, 16.0 and 32.0 at noise 4, 8, 16 and 32 times the turn rate; the simulation's log-log slope is 1.0021, and the exact slope is 0.9989. The physics skeptic, 20,000 arrows with exact rotations: 4.03, 8.14, 16.28, 31.93, slope 0.996; middle band 0.380. The watched-pot effect has been measured (Streed et al. 2006: 3.60 ± 0.43 against 4). The computation behind it is the fold 'Watching without reading' on the first shelf. Shared mathematics only: a system with choice is not a quantum particle. Run it yourself What you need Any watched system whose alignment with an observer's line can be tracked run by run, with a steady turn the same at every watching strength. The steps Watching strengths S, 2S, 4S and 8S, each at least 20 times the turn rate. Measure (a) hold time: when the group's mean alignment falls to 1/e; (b) the share of runs with |alignment| < 0.5 at the moment the mean has halved. It holds if Log-log slope of hold time against strength between 0.8 and 1.2 (computed 1.00), and a middle-band share of at least 0.25 (computed 0.383). It fails if A slope of 0.6 or less (inertia gives 0.5) or no growth; or a middle-band share of 0.05 or less with at least 0.15 of runs past −0.9 (the jump signature of a reading that sets the state: computed 0.000 and 0.256). Report Send: the hold times at each strength and the per-run alignment records. Where: a results form is coming. Sources and run files Bloembergen, Purcell and Pound 1948 Gagen, Wiseman and Milburn, PRA 48, 132 (1993) (opened) Streed et al. 2006 Slichter et al., NJP 18, 053031 (2016) (opened) Run files _build/gaps/RUNS_2026-10-01_02/pond_pond_result.json (research.W.test; vet corrections) _build/gaps/FIGURE_DATA_2026-10-02/pond_and_watched.json missing from the permanent copies: check_w.py (part 7: qubit runs), the physics skeptic's v_arrow.py and v_arrow.out, and the meaning skeptic's vm_w.py and vm_w_out.txt (the numbers are in pond_pond_result.json) What would refute it Hold time growing only as the square root of watching strength (slope 0.6 or less) or not at all; or runs that jump rather than creep (middle-band share 0.05 or less with at least 0.15 of runs past −0.9). See it The house: Drift The house: Testimony The geometry: Watched, not set open Does gravity arrive ahead of light from farther away? When two neutron stars merge, both a gravitational wave and light reach us. Einstein's theory says they travel at the same speed. One idea about a hidden fifth dimension lets gravity take a shortcut. Then gravity would arrive earlier from farther away. Timing many mergers at many distances tells the two apart. One event so far says the speeds agree within −3 parts in 10¹⁵ (gravity slower) to +7 parts in 10¹⁶ (gravity faster). Status open. Calibrated on GW170817 (2017), at about 40 megaparsecs: the physics skeptic set the corrected numbers (ℓ = 0.234 Mpc) to fit that event, so it cannot score this pre-registration. Not yet scored on a new event. Pre-registered 1 October from two sides (swing A1 and the per-dimension run). Who can score it: anyone, as arithmetic on public event data, whenever new mergers are seen in both. The mathematics Fit Δt = t_light − t_gravity = a + b·D/c, with a absorbing emission delays (about 10 s, flat in D). A warped bulk on an expanding brane gives a lead ∝ ℓ²z⁴/r ∝ D³ (Visinelli et al. 2018, eq. 20). A static asymmetric warp gives a lead roughly linear in D past a threshold (Chung and Freese, eq. 3). How it was checked GW170817: the light came 1.734 s after the gravitational wave over about 40 Mpc; the speeds agree within −3×10⁻¹⁵ to +7×10⁻¹⁶ (Abbott et al. 2017). Caps consistent with that event: ℓ < 0.099 Mpc if the whole gap is shortcut, ℓ < 0.25 Mpc with 10 s of emission slack. The builder first used Visinelli's 68% bound (0.535 Mpc), which predicts a 52 s lead at 40 Mpc, the very distance where 1.734 s was seen; the physics skeptic corrected the numbers to ℓ = 0.234 Mpc. That makes GW170817 the calibration, not a score. The grader notes the 'speeds equal' side is consensus physics, so a pass cannot single out the swing. An outside claim, Kletetschka 2025, prints Δv/c = (1.5 ± 0.3) × 10⁻¹⁵ and never defines the sign of Δv. If it means gravity faster than light, GW170817 excludes it (about 2.1 times above +7 × 10⁻¹⁶). If it means gravity slower, it fits inside the bound. Undecided. Run it yourself What you need Public catalogues of mergers seen in both gravitational waves and light; arrival times; the gravitational-wave distance D. The steps For every such event record Δt and D, and fit Δt against D. It holds if Speeds equal (swing A1 and Einstein): at least three events spanning 40 Mpc to at least 200 Mpc, with |b| < 10⁻¹⁵ and consistent with zero (10⁻¹⁵ shows as 20.6 s at 200 Mpc). Shortcut: gravity's lead rises with D (fitted power ≥ 1) and the farthest lead exceeds 10 s; a power near 3 names the warped bulk, near 1 the asymmetric warp. Corrected leads at ℓ = 0.234 Mpc: at most 10, 156, 1,250 and 10,000 s at 40, 100, 200 and 400 Mpc. It fails if Speeds equal: a trend |b| ≥ 10⁻¹⁴ at 3σ or more (103 s at 100 Mpc, 206 s at 200 Mpc), or any measured nonzero photon mass. Shortcut: no rise with D; one event at 200 Mpc with |Δt| < 10 s caps ℓ < 0.021 Mpc, 11 times tighter. Report The collaborations publish the events. Send: the event list with Δt and D, and the fit. Where: a results form is coming. Sources and run files Abbott et al., ApJL 848, L13 (2017), arXiv 1710.05834 (opened) Visinelli, Bolis and Vagnozzi, PRD 97, 064039 (2018) (opened) Chung and Freese, PRD 62, 063513, hep-ph/9910235 (opened) Caldwell and Langlois, gr-qc/0103070 (opened) Csáki, Erlich and Grojean, hep-th/0012143 (opened) Kletetschka 2025 (opened; the sign of Δv is not defined) Run files _build/gaps/RUNS_2026-10-01_02/perdim_perdim_result.json (light.test; vet_physics corrections) _build/gaps/FIGURE_DATA_2026-10-02/per_dimension.json _build/gaps/RUNS_2026-10-01_02/swings_swings_result.json (A1, graded) missing from the permanent copies: test_prereg.py and test_prereg.json, the skeptic's v5_brane_out.txt and v6_caps_out.txt, and swingA.py (the numbers are in perdim_perdim_result.json and swings_swings_result.json) What would refute it Equal speeds fail if the gap trends with distance, |b| ≥ 10⁻¹⁴ at 3σ or more. The shortcut fails if gravity's lead does not rise with distance. See it The house: The Two Clocks open Does gravity steepen below 38.6 micrometres? Suppose gravity leaks into hidden dimensions below some small size. Then its pull must fall off faster there. In three dimensions it falls as one over the distance squared. That law has been checked down to 52 micrometres. A steeper fall below that would mean extra dimensions at that scale. With more than three large dimensions, no orbit would be stable. This is the established test for extra dimensions. The house makes no prediction here. Its d counts the directions a system can aim in, not the dimensions of space. Status open. Pre-registered 1 October in the per-dimension run. Newton's law holds today from 52 µm to 3.0 mm. This is the established test for extra dimensions; the house makes no prediction here, because its d counts the directions a system can aim in, not the dimensions of space. Who can run it: a precision-gravity lab. The live figure · Count the dimensions Four: no orbit holds, light falls less than twice, a flash lingers, and a wanderer rarely comes home. Open it The mathematics Force ∝ 1/r^(2+k) below the size R of k extra dimensions; the n = 3 + k row of the per-dimension table governs there. How it was checked Lee, Adelberger et al., PRL 124, 101101 (2020): 1/r² fits from 52 µm to 3.0 mm; Yukawa ranges under 38.6 µm at 95%. Per-dimension table: orbits close only at n = 3; none is stable from n = 4 up (a 1% slowdown falls in after 1.13 orbits at n = 4); the skeptic reproduced 1.1282. Run it yourself What you need A torsion balance or micro-cantilever reaching below 38.6 µm. The steps Measure the slope of log(force) against log(separation) below 38.6 µm. It holds if The slope steepens from −2 to −(2 + k), with k a whole number of at least 1. It fails if The slope stays −2 at every separation reached. Report Send: force against separation, with errors. Where: a results form is coming. Sources and run files Lee, Adelberger et al., PRL 124, 101101 (2020), arXiv 2002.11761 (abstract, opened) Bertrand 1873 and Ehrenfest 1917, via Tegmark, gr-qc/9702052 (opened) Run files _build/gaps/RUNS_2026-10-01_02/perdim_perdim_result.json (ret.test, ret.claims) _build/gaps/FIGURE_DATA_2026-10-02/per_dimension.json missing from the permanent copies: orbits.py, orbits_result.json, RETURN_PER_DIMENSION_REPORT.md and the skeptic's v3_return_out.txt (the numbers are in perdim_perdim_result.json) What would refute it The force law stays 1/r² below 38.6 µm at every separation reached. See it The house: Concentration The house: The Flat Case The geometry: Count the dimensions open The pull of counting: does the dark pull's scale grow more slowly than the expansion rate? Galaxies show an acceleration scale. Below it, their rotation stops following the visible mass. A swing from the house predicts how that scale changes as we look further back. At redshift 2, it should be only about 1.22 times its value at redshift 1. If the scale simply tracked the expansion rate, the ratio would be about 1.68. One survey that measures both, by one method, would decide it. Status open; under pressure, not refuted. Pre-registered 1 October (swing B3), graded 'a swing that holds up'. Only the shape with redshift is predicted; the level is set from outside, and the room-to-wander constant in it is read off the dark-energy fit. Who can score it: anyone, once one survey publishes a₀ at z ≈ 1 and z ≈ 2 by one method. The mathematics Entropic pull F = +T dS/dx = −2CTx/(1 − x²) (sympy). Prediction a0(z)/a0(0) = (ρ_DE/ρ_DE0)·H/H0 with DESI+CMB+DESY5: 1.44 / 1.52 / 1.83 / 2.04 / 2.24 at z = 0.4 / 0.5 / 1 / 1.44 / 2. R = a0(2)/a0(1) = 1.224 (band 0.962–1.312 across DESI fits). How it was checked MUSE-DARK III (Ciocan et al., arXiv 2604.22613, 2026): a0 at z ≈ 1 = 2.38 (+0.12/−0.10)×10⁻¹⁰ m/s², with bins rising from about 1.99 to 2.71; the paper says a0 rises 'faster than that of H(z)'. Anchored on the local 1.20, the swing (B3) predicts 2.20 (8% low, 1.6σ statistical). Across their range the swing rises ×1.30 against their bins' ×1.36 (consistent); their global linear fit (slope/intercept 1.59 against the swing's 0.47) is in tension. Grader's caveats: 'line for line Verlinde' overclaims (same form only); only the redshift shape is predicted, the level is anchored; Verlinde's own law fails Solar-System perihelia (Hees, Famaey and Bertone 2017). The redshift shape uses C(z) ∝ ρ_DE(z), read off DESI. That is the identification from swing B2, which the fourth shelf lists as numerology. Run it yourself What you need One survey and one method at z ≈ 1 and z ≈ 2: JWST/NIRSpec or KMOS IFU, ALMA rotation curves, or MUSE-DARK extended. The steps Measure a0 in both bins; take R = a0(z=2)/a0(z=1), in which the normalisation cancels. It holds if R in [0.95, 1.40] with σ_R ≤ 0.12. It fails if R ≥ 1.50 at 2σ or more (H alone gives 1.68, MUSE's line 1.61), or R ≤ 0.80. Report Survey teams publish. Send: both a₀ values with their errors, and the method. Where: a results form is coming. Sources and run files Verlinde, JHEP 04 (2011) 029 and SciPost Phys. 2, 016 (2017) (opened) McGaugh, Lelli and Schombert, PRL 117, 201101 (2016) Brouwer et al., A&A 650, A113 (2021) (opened) Ciocan et al. (MUSE-DARK III), arXiv 2604.22613 (opened) DESI DR2 Results II, arXiv 2503.14738 (opened) Hees, Famaey and Bertone, PRD 95, 064019 (2017) (opened) Run files _build/gaps/RUNS_2026-10-01_02/swings_swings_result.json (B3, graded) missing from the permanent copies: the B/ folder and the grader's grade.py and grade_out.txt (the numbers are in swings_swings_result.json) What would refute it a₀(z = 2)/a₀(z = 1) ≥ 1.50 at 2σ or more, or ≤ 0.80. See it The house: The Measure open Can a crystal hear the electron's inner clock? In 1924 de Broglie said every particle carries an inner clock. For the electron, one tick lasts 8.09 × 10⁻²¹ seconds. Catillon's team read an 8% dip near 80.87 MeV/c in silicon, in 2008, as that tick. No other team has repeated it. Bauer (2014) argues ordinary channeling and Dirac motion account for it. In germanium and diamond, the dip must move to new places set by the spacing of the rows. A dip that moves with the row spacing still cannot separate the two readings. Status open. A dip reported once (Catillon et al. 2008) and read as the tick; Bauer (2014) disputes the reading; not repeated by another team. Pre-registered 1 October (swing A2), graded 'a swing that holds up', with one refute clause dropped. Who can run it: an accelerator lab with a channeling setup. The mathematics Resonance (mc²/h)/γ = v/d gives p = m c d/λ_C: a slope of 0.210607 MeV/c per pm of row spacing. How it was checked Catillon et al. 2008: an 8% dip within 0.5% of the resonance at 80.874 MeV/c in Si<110>; the predicted 80.880 is 0.007% from it. Bauer 2014 puts the observed resonance near 81.1 MeV (0.28% high), sees a 'W' angular pattern, and argues ordinary Dirac motion accounts for it. Grader: a dip that moves with d would confirm a clock at the mc²/h scale, but cannot separate 'a lap around a hidden direction' from Dirac's own oscillation; the hidden circle adds no number. One shared circle for all particles is out: m_μ/m_e = 206.768283 is 50,370σ from a whole number. Run it yourself What you need Thin crystals (about 1 µm) in at least two row spacings, e.g. Si<110> with Ge<110> or diamond<110>; an electron beam scanned near the resonances. The steps 0-degree electron transmission, scanned in momentum steps of 0.1% or finer. It holds if A dip of at least 3% depth at 5σ or more in each crystal, within ±0.5% of p = 0.210607 MeV/c per pm × d (Si<110> 80.88, Ge<110> 84.26, diamond<110> 53.12 MeV/c), with a fitted slope of 0.2106 ± 0.002. It fails if The Si<110> dip not reproduced at 3σ with four times the 2008 counts; or the dips do not scale with d (e.g. Ge<110> outside 83.84–84.68 while Si<110> sits at 80.88). Report Send: transmission against momentum for each crystal. Where: a results form is coming. Sources and run files de Broglie 1924 Catillon et al., Found. Phys. 38, 659 (2008) (opened) Gouanère et al. 2005 Bauer, arXiv 1409.0888 (2014) (opened) Lan et al., Science (2013) Run files _build/gaps/RUNS_2026-10-01_02/swings_swings_result.json (A2, graded) missing from the permanent copies: swingA.py (§2, §4) and the grader's grade_out.txt (the numbers are in swings_swings_result.json) What would refute it Silicon's dip does not return at 3σ with four times the 2008 counts, or the dips do not move with row spacing. A dip that moves confirms a clock at the mc²/h scale; it cannot tell a lap around a hidden direction from Dirac's own motion. See it The house: The Two Clocks open Held by two: check the four-dimension result with your own code Let a system with choice keep its alignment with the truth and with one other reference, and still move. It needs four directions to aim in. In three it can keep both only by standing still. In four it can keep both while it turns, in the one plane at right angles to both references. Under the house's own pull, two references it faces pull as one, toward a blend of the two. Then it circles the blend, and in three directions one alignment rises as the other falls. Anyone who codes can check this. Status open. Unrun by anyone outside. Pre-registered 2 October. Its skeptic has reported and the core held, checked with the skeptic's own code; the skeptic added the summed-pull scope and a house-law arm, now in the protocol below. The fold "Pulled by two" is live in The Return. A check of the mathematics, not a test in the world. Who can run it: anyone who codes, in an afternoon. The live figure · Pulled by two Circling the blend at 0.8: each line-up swings between 0.141 and 0.990, one rising as the other falls. Their sum holds at 1.131. In four directions the same circle, laid in the free plane, holds each at 0.566. Open it The mathematics The builder's pull: U = −Σ gᵢ a·M̂ᵢ − 0.3 Σ_{i