The situation
docs/STATUS.md carries a long list of C3 results — scored, prospective, several of them
prospectively falsified, which is the strongest kind this project produces. None of them is
written up. The implicit reason has been that a write-up should wait until the pieces cohere
into one story about p_c, state dimension, and CFT identity at once.
#615 removed that expectation: bounded finite-horizon task rank has no threshold content
without critical-sector completeness. The unified story is not arriving on the current
evidence, and two results that are already complete should not be held hostage to it.
Neither of these needs a new computation. This is a writing ticket.
Paper 1 — the matching-odd finite-size signal, and the failure of scalar closure
The whole arc is already scored and committed:
global zero rejected chi2 = 31.1857355515 / 4, p = 2.81e-6
(independent P43 + P57 primary synthesis)
fixed H4 predictions hold 3.4622795373 / 4, p = .484
frozen norm-5 H4 beats aliases H4 0.4163/2 H12 35.1931/2 H8 16.0120/2
one scalar multiplier FAILS three-level transfer 9.3520/2, p = .0093
one scalar width FAILS full-covariance norm-5 width 24.5004/10
pure P4[S'] ~ N^-5/4 FAILS prospectively, 52.71634/2 on P48's new geometry
frozen center-slope correction predicts N290 at z = -0.666, bare 2^(3/8) at z = -22.690
That is a coherent, honest paper: a real matching-odd orientation signal exists at finite
size, a frozen H4 transfers, and every attempt to close it with a single scalar — multiplier,
width, or exponent — is prospectively falsified. The negatives are the contribution. It
does not need to explain p_c and should not try.
Add, as the methodological spine rather than as separate claims: the exact channel
correction DeltaS_cross = -DeltaS_either (0.5700315436/2), the finite Russo identity, and
the frozen-prediction discipline that makes the falsifications count.
What must be in it, and what a reader will otherwise ask: the correlated-block accounting
(GOVERNANCE §2E — these are repeated views of overlapping raw blocks and must be counted
once), and the aspect-ladder result as an explicit limitation (#577: underpowered, three
surviving hypotheses).
Paper 2 — exact continuation, branching, and the bounded-state no-go
The second cluster is exact rather than statistical, which makes it a different paper with a
different audience:
#435 / #491 / #549 / #550 cut-network results: richer branching futures require
unbounded predictive classes
#615 bounded finite-horizon task rank has no threshold content
without critical-sector completeness -- two analytic Markov
families, identical finite-horizon response, thresholds at
1/2 and 1/3
#598 / #600 exact reflection quotient, first-order-invisible symmetry
breaking, balanced realization factoring through the quotient,
odd sector exactly inert
The through-line is sharp and, per #601, partly novel: what a bounded state can and cannot
carry, with an exact symmetry quotient on one side and a constructive no-go on the other.
#601 established that the selection-rule statement for equivariant Markov generators has no
named prior art, so there is a small genuine contribution of language there.
Boundaries the draft must respect, all already established:
- The noncrossing reflection-fixed count is classical — Callan-Smiley Thm 1 plus Burnside,
with Ding 2016 for the even-n classes. Cite, do not claim.
- "Coarsest lumping = automorphism-orbit partition" is not a theorem in general
(D'Angeli-Donno 2013 Prop. 13). Our w = 4..8 agreement is an instance and must be called
one.
- P398 is a calibration process, not percolation. The paper must say so in its own voice, not
in a footnote.
Journal
Paper 2 is the more novel and the more defensible; it should go first if only one can be
prepared. I will pick venues once drafts exist — that decision is not blocking and should
not be used as a reason to delay drafting.
Deliverable
1. two drafts, each standing alone, neither claiming the other's ground;
2. every number traced to a committed artifact path, not retyped from a note;
3. an explicit limitations section in each, with the correlated-block accounting;
4. a list of what had to be left out, so the next draft knows where to start.
Claim boundary
- No new computation. If a draft needs a number that does not exist, that is a finding —
report it rather than producing it here.
- Do not promote anything in
docs/STATUS.md as part of drafting. Levels change on evidence,
not on prose.
- Do not merge the two papers. They have different evidence types and different audiences,
and the reason nothing has been written is precisely the habit of merging them.
Related: #553, #557, #615, #598, #600, #601, #577, #275.
The situation
docs/STATUS.mdcarries a long list ofC3results — scored, prospective, several of themprospectively falsified, which is the strongest kind this project produces. None of them is
written up. The implicit reason has been that a write-up should wait until the pieces cohere
into one story about
p_c, state dimension, and CFT identity at once.#615 removed that expectation: bounded finite-horizon task rank has no threshold content
without critical-sector completeness. The unified story is not arriving on the current
evidence, and two results that are already complete should not be held hostage to it.
Neither of these needs a new computation. This is a writing ticket.
Paper 1 — the matching-odd finite-size signal, and the failure of scalar closure
The whole arc is already scored and committed:
That is a coherent, honest paper: a real matching-odd orientation signal exists at finite
size, a frozen H4 transfers, and every attempt to close it with a single scalar — multiplier,
width, or exponent — is prospectively falsified. The negatives are the contribution. It
does not need to explain
p_cand should not try.Add, as the methodological spine rather than as separate claims: the exact channel
correction
DeltaS_cross = -DeltaS_either(0.5700315436/2), the finite Russo identity, andthe frozen-prediction discipline that makes the falsifications count.
What must be in it, and what a reader will otherwise ask: the correlated-block accounting
(GOVERNANCE §2E — these are repeated views of overlapping raw blocks and must be counted
once), and the aspect-ladder result as an explicit limitation (#577: underpowered, three
surviving hypotheses).
Paper 2 — exact continuation, branching, and the bounded-state no-go
The second cluster is exact rather than statistical, which makes it a different paper with a
different audience:
The through-line is sharp and, per #601, partly novel: what a bounded state can and cannot
carry, with an exact symmetry quotient on one side and a constructive no-go on the other.
#601 established that the selection-rule statement for equivariant Markov generators has no
named prior art, so there is a small genuine contribution of language there.
Boundaries the draft must respect, all already established:
with Ding 2016 for the even-
nclasses. Cite, do not claim.(D'Angeli-Donno 2013 Prop. 13). Our
w = 4..8agreement is an instance and must be calledone.
in a footnote.
Journal
Paper 2 is the more novel and the more defensible; it should go first if only one can be
prepared. I will pick venues once drafts exist — that decision is not blocking and should
not be used as a reason to delay drafting.
Deliverable
Claim boundary
report it rather than producing it here.
docs/STATUS.mdas part of drafting. Levels change on evidence,not on prose.
and the reason nothing has been written is precisely the habit of merging them.
Related: #553, #557, #615, #598, #600, #601, #577, #275.