From e00b00acfe5c5571fc3ee4d90b784fe00c82cfd6 Mon Sep 17 00:00:00 2001 From: "copilot-swe-agent[bot]" <198982749+Copilot@users.noreply.github.com> Date: Mon, 3 Aug 2026 10:52:44 +0000 Subject: [PATCH] generator: 4 new speculations (co-emergence x3, ggd x1) --- ...ce-ftoy-attractive-coupling-subcritical.md | 81 +++++++++++++++++ .../ce-mass-phase-residual-in-ggd-kernel.md | 88 +++++++++++++++++++ .../ce-second-iterate-radius-power-law.md | 64 ++++++++++++++ .../ggd-cpmg-odd-even-colored-asymmetry.md | 81 +++++++++++++++++ 4 files changed, 314 insertions(+) create mode 100644 programs/co-emergence/claims/ce-ftoy-attractive-coupling-subcritical.md create mode 100644 programs/co-emergence/claims/ce-mass-phase-residual-in-ggd-kernel.md create mode 100644 programs/co-emergence/claims/ce-second-iterate-radius-power-law.md create mode 100644 programs/gaussian-gravitational-decoherence/claims/ggd-cpmg-odd-even-colored-asymmetry.md diff --git a/programs/co-emergence/claims/ce-ftoy-attractive-coupling-subcritical.md b/programs/co-emergence/claims/ce-ftoy-attractive-coupling-subcritical.md new file mode 100644 index 0000000..89aaee2 --- /dev/null +++ b/programs/co-emergence/claims/ce-ftoy-attractive-coupling-subcritical.md @@ -0,0 +1,81 @@ +--- +id: ce-ftoy-attractive-coupling-subcritical +program: co-emergence +tier: speculation +status: live +statement: > + For real gamma > 0 (attractive self-consistency weighting, the sign opposite + every instance tested to date, all fixed at gamma = -1 or -2) F_toy's unique + fixed point loses stability through a subcritical flip bifurcation rather + than the supercritical one established at gamma = -1: onset produces a + finite-amplitude jump to a period-2 cycle, with a finite beta-window of + bistability (stable fixed point and stable cycle coexisting) below the + crossing, rather than a continuous cycle-amplitude bound growing + continuously as sqrt(beta - beta_flip) from zero. +object: + name: F_toy + definition: "F(psi)_sigma = exp(gamma R_sigma(psi)) / ||exp(gamma R(psi))||_2" + space: the probability simplex (real branch, gamma real) +hypotheses: + - gamma real and strictly positive + - A symmetric + - h in R^N + - beta swept across the flip eigenvalue crossing at -1 +depends_on: + - id: ce-toy-fixed-point-multiplicity + role: context + transfers: same-object + justification: > + Same object F_toy; explicitly not the same question. That dead + speculation asked whether a SECOND fixed point of F exists at the + cycling parameters (killed: exactly one root found by exhaustive + root-finding). This asks whether a second stable ATTRACTOR (a cycle) + can coexist with the unique fixed point in a finite parameter window - + a bistability question the multiplicity search did not address, since + it searched for additional roots of F, not additional attracting sets + of the iteration. + - id: ce-riem-classical-unique + role: context + transfers: same-object + justification: > + Same F_toy object at a different, unexplored sign of gamma; the + uniqueness claim there is stated and evidenced only for the tested + gamma = -1, -2 branch and does not cover gamma > 0. +falsifier: > + Track the cycle amplitude near the flip crossing for several gamma > 0 + values; a continuous onset with amplitude growing as sqrt(beta - beta_flip) + from exactly zero, matching the gamma = -1 supercritical result, or the + absence of any beta-window where both the fixed point and a period-2 cycle + are simultaneously stable under forward and backward beta sweeps, falsifies + the subcritical claim. +consequence: > + A subcritical transition would mean self-consistency selection is + history-dependent (hysteretic) for attractive coupling: which configuration + F_toy's iteration lands on would depend on initial conditions near the + transition, not only on beta and gamma. That is a genuinely different + selection-principle gap from the multiplicity question already closed + (a second fixed point), and would matter for any argument that treats "the" + self-consistent solution as the map's unique attractor rather than merely + its unique fixed point. +provenance: {born: 2026-08-03, born_by: generator} +--- + +Every real-gamma instance in the record — [[ce-toy-fixed-point-multiplicity]], +[[ce-riem-classical-unique]], [[ce-second-iterate-real-spectrum]] — fixes +gamma at -1 or -2 (repulsive self-consistency weighting: R appears with a +negative sign in the exponent). The opposite-sign branch has not been swept in +any recorded instance. Bistability (coexisting fixed point and cycle) is a +structurally different failure mode from the multiplicity question the +generator already asked and lost: that speculation was about a second FIXED +point of F; this is about a second stable ATTRACTOR of the iteration, which a +uniqueness-of-fixed-points result does not by itself exclude. + +Axiom check: purely an internal statement about the toy model's Riemannian +branch (gamma real, theta = 0); no background metric, foliation, or time +parameter is invoked — F_toy is a discrete self-map, and "history-dependence" +here means dependence on the iteration's starting point, not on any physical +time evolution. No axiom violation is apparent. Flagged honestly: if +subcritical, describing the outcome as "selection" already presupposes F_toy's +iteration is the relevant dynamical process picking out the physical +configuration, a reading the paper's own framing licenses but this claim does +not re-derive. diff --git a/programs/co-emergence/claims/ce-mass-phase-residual-in-ggd-kernel.md b/programs/co-emergence/claims/ce-mass-phase-residual-in-ggd-kernel.md new file mode 100644 index 0000000..29f8380 --- /dev/null +++ b/programs/co-emergence/claims/ce-mass-phase-residual-in-ggd-kernel.md @@ -0,0 +1,88 @@ +--- +id: ce-mass-phase-residual-in-ggd-kernel +program: co-emergence +tier: speculation +status: live +statement: > + Because mass requires Lorentzian signature (ce-mass-signature) and Lorentzian + signature carries the complex self-consistency phase theta (the CE-10 + theta-signature identification), a genuinely massive two-branch superposition + cannot supply the gaussian-gravitational-decoherence noise kernel + N_0000(x, x') exactly as the real bilinear (c^4/4) Delta_rho(x) Delta_rho(x') + that ggd-noise-kernel derives: writing each branch's expected stress-energy + with its self-consistency-weight phase factor explicit produces a residual + term of order sin(theta) that survives in N_0000 for any pair of branches + whose co-emergence phases differ, vanishing only in the theta -> 0 + (Riemannian, hence per ce-mass-signature formally massless) limit. +object: + name: N_0000(x, x'), decomposed via each branch's self-consistency phase theta + space: expectation values of the stress-energy operator T00 over the two branches entering the Einstein-Langevin analysis +hypotheses: + - each branch is a genuinely massive configuration (Lorentzian per ce-mass-signature) + - a curved, dynamical, generically symmetry-free 4-manifold + - each branch's co-emergence phase theta is well defined and, in general, differs between the two branches + - non-relativistic stress-energy operator T00 = c^2 rho(x - X_CM) + - orthogonal branches + - each branch has definite centre-of-mass position +depends_on: + - id: ce-mass-signature + role: load-bearing + transfers: cross-object + justification: > + Different object (a particle-classification argument on a curved + manifold vs. an expectation-value calculation on branch densities); the + claim borrowed is the identification mass <-> Lorentzian signature, not + any structure of the mass-shell argument itself. Note this dependency + currently carries an audit verdict of "demote" (Wigner's flat-space + classification applied to a curved, generically symmetry-free + manifold); this speculation is exposed to that same gap and does not + independently repair it. + - id: ggd-noise-kernel + role: load-bearing + transfers: cross-object + justification: > + Different object (a semiclassical stress-energy expectation-value + identity vs. this speculation's proposed phase-dependent correction to + it); the two formalisms have never been checked for mutual consistency + across the program boundary, which is exactly what this speculation + tests. +falsifier: > + Recompute N_0000 keeping the self-consistency phase explicit in each + branch's T00 expectation value (writing the branch amplitude with its + e^{i theta} weight factor rather than treating Delta_rho as a real classical + density difference from the outset). Expectation values of a Hermitian + operator in any physical state are real by construction; if the phase + factors cancel identically for exactly this reason, with no residual + sin(theta) surviving in N_0000 to any order, the speculation is falsified + outright. +consequence: > + If a real residual term survives, GGD's noise kernel is incomplete for any + branch pair with differing co-emergence phase, predicting an additional + decoherence channel set by theta rather than by Delta_rho alone - + potentially discriminating from Delta_rho-only. If the residual does not + survive (the more likely outcome a priori, given that T00 expectation + values are manifestly real), this would be the first explicit check that + co-emergence's mass/signature construction and GGD's stress-energy + construction are mutually consistent where they overlap - a cross-program + consistency question neither program's record currently addresses. +provenance: {born: 2026-08-03, born_by: generator} +--- + +A cross-program consequence: no existing claim connects co-emergence's +mass-signature identification to gaussian-gravitational-decoherence's noise +kernel, and the two frameworks have never been checked against each other at +the point where they should overlap - both concern the stress-energy content +of a massive superposition. + +Axiom check, stated honestly rather than resolved: combining the two +requires specifying at what point in "time" theta is evaluated, since GGD's +T00 expectation value is defined at a Schrödinger-picture instant on a fixed +background time slice, while co-emergence's theta is a property of a +self-consistent FIXED POINT of a timeless map, not of a state's evolution. +Treating "the branch's theta at the moment N_0000 is evaluated" as +well-defined risks smuggling a preferred-time identification between GGD's t +and co-emergence's fixed-point locus that neither program's axioms license. +This is flagged as a genuine hole in how the two objects would even be +compared, not resolved here - a speculation that violates an axiom in its own +construction is still worth proposing, per the generator's own criteria, +provided the violation is named rather than hidden. diff --git a/programs/co-emergence/claims/ce-second-iterate-radius-power-law.md b/programs/co-emergence/claims/ce-second-iterate-radius-power-law.md new file mode 100644 index 0000000..1d05082 --- /dev/null +++ b/programs/co-emergence/claims/ce-second-iterate-radius-power-law.md @@ -0,0 +1,64 @@ +--- +id: ce-second-iterate-radius-power-law +program: co-emergence +tier: speculation +status: live +statement: > + The second-iterate spectral radius rho_2(beta) of D(G o G) at the F_toy + attracting fixed point decays as a power law rho_2(beta) ~ C beta^{-1} for + beta well past the flip onset, with C independent of N, driven by the + Jacobian's spectral weight concentrating onto a single direction aligned + with the dominant softmax component as the fixed point sharpens toward a + simplex vertex. +object: + name: D(G o G) + definition: "D(G o G)(a) = S(e) M S(b) M, with S(p) = diag(p) - p p^T, b = G(a), e = G(b)" + space: tangent space of the probability simplex +hypotheses: + - gamma real + - gamma = -1 + - the marginal-coupling matrix A symmetric + - the softmax form induced by the self-consistency weight + - beta swept at least two orders of magnitude past the flip onset + - h in R^N +depends_on: + - id: ce-second-iterate-real-spectrum + role: load-bearing + transfers: same-object + justification: > + Same object, D(G o G); this speculation proposes a specific rate for the + decay that claim's own gaps field records as unexplained ("does not + explain WHY the second-iterate spectral radius decays to ~0.037 rather + than merely staying below 1"). +falsifier: > + Fit log(rho_2(beta)) against log(beta) across at least two decades of beta at + several N; a fitted exponent that is not close to -1 (say outside + [-1.3, -0.7]), or that drifts systematically with N, falsifies the power law + as stated. The recorded data point rho_2 ~ 0.037 near beta ~ 50 is a single + sample and does not by itself confirm or refute a specific exponent. +consequence: > + A clean inverse-beta law would give the missing mechanism the parent claim + flags as absent (the failed Rayleigh-quotient bound diverges instead), and + would let ce-riem-classical-unique's bound on the exact-to-bound contraction + ratio be re-derived analytically rather than only observed to fall to + 1e-310 at large beta. A non-power-law or N-dependent exponent would instead + show the decay is not a single universal mechanism, narrowing what + ce-second-iterate-real-spectrum's palindrome argument can be said to explain. +provenance: {born: 2026-08-03, born_by: generator} +--- + +Mined from [[ce-second-iterate-real-spectrum]]'s own gaps field and the +Rayleigh-quotient failure recorded on [[ce-riem-classical-unique]] ("the bound +diverges... because the smallest eigenvalue of S(e) tends to zero as the cycle +concentrates near a simplex vertex"). That failure is itself evidence for the +concentration mechanism proposed here, but a divergent bound is not a +convergent rate, and no exponent has been fit. + +Axiom check: this is a purely internal statement about the toy model's +Jacobian at gamma real (Riemannian branch, theta = 0); it does not invoke a +background metric, a preferred foliation, or unitary time evolution — F_toy is +iterated as a discrete self-map with no time parameter involved. No axiom +appears to be smuggled. The one honesty flag: "concentrating near a simplex +vertex" describes the *attracting* orbit's location, which is itself an +empirical fact about this map (not assumed here), carried over unchanged from +the parent claim's evidence record. diff --git a/programs/gaussian-gravitational-decoherence/claims/ggd-cpmg-odd-even-colored-asymmetry.md b/programs/gaussian-gravitational-decoherence/claims/ggd-cpmg-odd-even-colored-asymmetry.md new file mode 100644 index 0000000..3e9bfd3 --- /dev/null +++ b/programs/gaussian-gravitational-decoherence/claims/ggd-cpmg-odd-even-colored-asymmetry.md @@ -0,0 +1,81 @@ +--- +id: ggd-cpmg-odd-even-colored-asymmetry +program: gaussian-gravitational-decoherence +tier: speculation +status: live +statement: > + Against a genuinely colored (non-static, non-delta-PSD) gravitational noise + spectrum with a finite correlation time - unlike the exactly-static kernel + that made ggd-cpmg-degeneracy vacuous - CPMG-n coherence recovery shows a + measurable odd/even asymmetry in the pulse count n: odd-n filter functions + retain a residual x^2 factor (F ~ x^4 / (64 n^4)) that even-n sequences + algebraically cancel (F ~ x^6 / (256 n^4)), so two CPMG sequences with + matched total duration and pulse spacing but n and n+1 pulses would show + measurably different coherence-recovery magnitudes, providing a diagnostic + of the noise spectrum's shape that does not require resolving which + mechanism sets its correlation time. +object: + name: filter-function overlap integral for a CPMG-n sequence against a colored noise power spectral density + space: single-qubit (or matter-wave interferometer) coherence under the Einstein-Langevin Gaussian-noise model already adopted by this program +hypotheses: + - the noise kernel has some genuinely finite correlation time tau_c (i.e. is not the exactly-static single-realization kernel of ggd-single-realization) + - CPMG pulse sequences with n and n+1 pulses at matched total duration T and matched inter-pulse spacing T/n vs T/(n+1) + - the power spectral density is colored (not white, not an exact Lorentzian where the asymmetry may wash out - see falsifier) +depends_on: + - id: ggd-cpmg-degeneracy + role: context + transfers: same-object + justification: > + Same object (CPMG filter functions against this program's noise + kernel), explicitly a different regime. The dead claim's own defense + pass derived the odd/even structural finding used here (odd n gives + F ~ x^4/(64 n^4), even n gives x^6/(256 n^4)) but only evaluated it + against the exactly-static kernel, where the PSD is a delta function + at zero frequency and every sequence (odd or even, any n) gives + identically zero filter response - the degeneracy that killed the + claim. This speculation asks whether the same structural asymmetry + survives once the kernel is genuinely colored, a regime the dead claim + never reached. +falsifier: > + Compute the filter-function overlap integral for a specific colored PSD + (the Lorentzian crossover form entering ggd-material-crossover, or a + generic 1/f^alpha form) at matched n and n+1. If the ratio + F_odd(n) / F_even(n) tends to 1 as the spectral content moves away from the + IR-cutoff-dominated regime where the dead claim's law was derived - i.e. + the odd/even structural difference is subleading to the overall n^-4 decay + common to both parities for realistic tau_c - the diagnostic is falsified + as practically useless, independent of whether the asymmetry exists in + principle. +consequence: > + If the asymmetry survives at a computable magnitude, it gives an + experimentally accessible pulse-count-parity diagnostic for the shape of + the gravitational noise spectrum that is orthogonal to, and available + before, the open GGD-1 material-crossover question - it needs only that + some finite tau_c exists, not which phonon (or other) mechanism sets it. + If it washes out, that sharpens ggd-cpmg-degeneracy's negative result: the + odd/even structure found there would then be an artifact of the IR-cutoff + convention specifically, not a generic feature of pulse-sequence filtering + against colored gravitational noise. +provenance: {born: 2026-08-03, born_by: generator} +--- + +Mined directly from [[ggd-cpmg-degeneracy]]'s tombstone: its defense pass +derived the odd/even structural finding as a correction to the attacking +pass's exponents, in service of showing the degeneracy claim was vacuous under +a static kernel - but the structural finding itself was never evaluated +against any colored spectrum, only flagged as mattering "for 1/f-type peaked +spectra" and washing out "against a Lorentzian" in the one comparison made. +That comparison was for a single fixed n, not the n-vs-(n+1) asymmetry +proposed here. + +Axiom check: this stays entirely within the program's existing +Einstein-Langevin / Gaussian-noise Assumption 1 and the Diosi-Penrose-style +kernel already adopted; it introduces no new background structure, preferred +frame, or foliation. It is conditional on the currently open question of +whether tau_c is finite at all (GGD-1, halted under needs-human) but is +explicitly agnostic to which mechanism sets tau_c - phonon, amplitude +suppression, or otherwise - unlike that milestone, which turns on identifying +the mechanism. This claim would still need that some finite-tau_c regime +exists to have any content; if GGD-1 resolves toward "no accessible platform +reaches the crossover," this speculation would be moot for realistic +platforms even if its filter-function mathematics is correct in principle.