canonical_seed_posting_of_operation
plain-language theorem explainer
A full multilevel posting operation on a nontrivial hierarchy projects to the seed-pair certificate used by the T5→T6 bridge. Anyone who already has adjacent-level posting with additive sizes obtains the seed posting at index post(0,1) for free. The proof is a direct field projection: post(0,1)=2 and size additivity on levels 0 and 1.
Claim. Let $M$ be a nontrivial multilevel composition (positive level sizes, at least three levels). Let $\mathrm{post}:\mathbb{N}\times\mathbb{N}\to\mathbb{N}$ be a canonical posting operation on $M$: $\mathrm{post}(0,1)=2$ and $M.(\mathrm{levels})(\mathrm{post}(i,j))=M.(\mathrm{levels})(i)+M.(\mathrm{levels})(j)$ for all $i,j$. Then $\mathrm{post}(0,1)$ carries a canonical seed posting operation on $M$ (seed index is the canonical second-order index $2$, lands at level $2$, and the posted seed size is additive).
background
The Unified Forcing Chain module derives T0–T8 as inevitabilities from the Recognition Composition Law plus normalization and calibration. The T5→T6 step forces $\varphi$ as the self-similar fixed point of a discrete ledger hierarchy.
A nontrivial multilevel composition $M$ supplies a positive size function on levels with at least three occupied levels. A canonical posting operation is a Prop-valued certificate on a map $\mathrm{post}$: posting the seed pair $(0,1)$ lands at level $2$, and posting is additive on level sizes for every pair.
The seed posting certificate is the weaker local datum the hierarchy recurrence actually uses: only the primitive closure of levels $0$ and $1$ at index $2$ with additive size. The full all-pairs operation is stronger than the T5→T6 bridge needs; this theorem isolates the projection.
proof idea
Term-mode structure construction for CanonicalSeedPostingOperation M (post 0 1). The three fields are filled directly from the full operation:
seed_index: fromop.post_zero_oneviasimpawith the definition of the canonical seed post index (sopost 0 1 = 2witnesses the index certificate).post01_eq_two: exactlyop.post_zero_one.seed_level_posting: specializeop.level_postingat $(0,1)$.
No auxiliary lemmas beyond the structure fields and the seed-index definition.
why it matters
The T5→T6 bridge in the forcing chain needs only seed-pair posting, not a full all-pairs operation. This projection removes an arbitrary post01 parameter from the hierarchy bridge: the index is forced to the canonical value $2$. Downstream hierarchy and $\varphi$-forcing arguments can therefore assume the weaker seed certificate whenever a full canonical posting is already in hand.
In the primer landmarks this sits under T5 (unique $J$) feeding T6 ($\varphi$ as self-similar fixed point on the discrete ledger). The module's stronger claim is a complete inevitability chain from the cost foundation; local posting additivity is part of the discrete hierarchy that makes self-similarity force $\varphi$ rather than an arbitrary scale.
No used_by edges are recorded yet; the declaration is infrastructure for the seed-level bridge rather than a cited leaf theorem.
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