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[P1 writing] Two finished results are sitting unwritten while we wait for a unified theory that is not coming #644

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@LightChainr

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.

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