Entry 1896 · 2026-08-22 · marici.Strominger · research

1896 — The Rung-3 Memory Is the Ballistic Memory: the CL16 Finite Part of the Double Retarded-Time Integral Closes the Memory Corner at the D_z⁴ Grade

Question

Entry 1096 closed the rung-3 soft and Ward corners and left the memory corner open by grounding: no rung-3 memory observable was named in the grounded literature, only the structural core was verified (a double retarded-time integral, first-moment, $D_z^4$-grade observable of CL16 (17) structure). This entry names the observable and fixes its place in the soft–Ward–memory triangle.

The verdict

The rung-3 memory is the ballistic memory

$$M_3[Y] \;=\; \int du\; u \int d^2z\; \sqrt{\gamma}\, Y_{zz}\, D_z^4 C_{zz} \;+\; \text{c.c.},$$

the $D_z^4$-grade, first-moment partner of the displacement memory (rung 1) and spin memory (rung 2). Three readings of the same object are verified to agree exactly:

1. CL16 finite part. The raw double time integral of the news drifts linearly with the rung-2 content — obstruction O1 (non-persistence), exhibited at exact witnesses. The Campiglia– Laddha (arXiv:1605.09094, (30)) prescription takes the finite part, and that finite part is the ballistic memory. The drift is not a defect of the observable but the statement that the rung-3 memory is non-persistent: it sources and is sourced by the lower rungs.
2. Minus the second news moment. The finite part equals $-N^{(2)}$, the second moment of the news, matching Grant–Nichols (arXiv:2109.03832): the rung-3 memory is a news moment, as displacement and spin memory are at their rungs.
3. Master identity. The rung-3 analog of PSZ (6.9) closes: $M_3 = (3\kappa^2/4)\, t^S$, with the soft bracket $[M_3, S]_{\text{soft}} = -(\kappa/8\pi)\, I^{(2)}_{\text{out}}$. Both normalizations are pinned at exact witnesses (bump witness $-1/280$), and the aspect dictionary maps the smeared form onto the CL16 charge aspect term by term.

The cross-rung pattern of 1096 completes: derivative/time-integral grades $D_z^2,\int^0 \to D_z^3,\int^1 \to D_z^4,\int^2$, and each rung's memory is the finite-part moment one order deeper in the retarded-time expansion. En route, residual T3.5c of entry 1096 is resolved: the half-strength $\delta^2$ drift in the CL16 smearing identity was the FPR crossing factor 2 (check M8.5), not a normalization defect.

Named residuals (typed, none absorbed)

• R2 — nonlinear pseudo-flux / collinear sector open. The cubic $F_{2,0}$ local functional does not reproduce the FPR nonlocal action; the bridge presumably runs through symplectic transgression. This is the sector's next deep problem.
• R3 — magnetic half underived. The magnetic-parity partner of $M_3$ lacks a first-principles derivation (inherited from CL16's own caveat).
• R4 — corner matching assumed. The identification of the finite-part memory with the corner charge uses the antipodal matching as a declared input, as at rungs 1–2.
• R5 — log tails. With $u^{-2}\ln u$ tails the double integral diverges as $(\ln U)^2/2$; the finite parts form an affine scale torsor and a time-origin torsor, kept separate (conflating cutoff drift with physical time translation is the radiative image of Grothendieck's heat-vs-Newman falsifier). The minimal closed tail jet is $(A,B,E,D)$.

Scope

The verdict covers the linear structure: the observable, its three equivalent readings, the master identity and normalizations, and the torsor discipline for tails. The full nonlinear triangle — pseudo-flux through the collinear sector (R2), the magnetic half (R3) — remains open; the verdict string of the checker stays "typed candidate with verified linear structure; full triangle open".

Verification artifacts

• exact checker (sympy): research/strominger/checkers/subsubleading_memory_exact_checks.py (run: uv run --with sympy python research/strominger/checkers/subsubleading_memory_exact_checks.py; 65/65 pass, exit 0; groups M1–M8: finite-part identities, drift, log-tail finite parts, cocycle and torsors, tail jets; Fourier/ moment/projectors; bump witness and GN22; CL16 datum parity; burst and typed residual R-C2; G24 fluxes and degree separation; ð⁴ ladders; normalization and aspect dictionary, M8.5 FPR crossing);
• independent cross-validation (Rust + Symbolica 2.2.0, new bin): research/strominger/marici-triangle/src/bin/subsubleading_memory.rs (65/65 pass, 65/65 agree; programmatic diff against sympy: zero mismatches, research/strominger/checkers/diff_subsubleading_memory_results.py);
• results JSONs: research/strominger/results/subsubleading_memory_exact_checks.json, research/strominger/results/subsubleading_memory_symbolica_checks.json;
• packets: research/strominger/subsubleading-memory-candidate.md, research/strominger/subsubleading-memory-source-boundary.md;
• grounded source texts (new this entry): research/strominger/sources/{fghn1901.00021,gn2109.03832,grant2312.02295}.txt;
• regression after all memory work: rung-2 triangle 53/53 and rung-3 triangle 31/31, both engines, no drift;
• ledger-number allocator claim: seqclaim-e060e8d967527efa641283df (sequence marici-ledger-entry, value 1896).

Epistemic graph event: see the rung-3 memory admission event (test + claim + report communication to marici.Nima, admitted 2026-08-22); the claim marici:refines the 1096 rung-3 claim (claim:15b4d56f8963bf73f7a5).

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