canonical_seed_post_index
plain-language theorem explainer
The canonical hierarchy level at which the two seed levels 0 and 1 are posted together is fixed as the natural number 2. Anyone working the multilevel composition or additive seed-posting models in the unified forcing chain cites this constant. It is a bare definition, not a derived theorem: local second-order closure of seeds 0 and 1 lands at the next index.
Claim. The canonical seed-posting index is the natural number $2$: the first local closure level at which the adjacent seed levels $0$ and $1$ of a second-order hierarchy are posted together.
background
The Unified Forcing Chain module derives T0–T8 as inevitabilities from the Recognition Composition Law, normalization, and calibration. Inside that chain, multilevel composition needs a distinguished place where the two primitive seed levels close.
A local second-order hierarchy begins with seed levels 0 and 1. Their first local composite is the next natural number. The additive seed-posting model later reads level sizes from event sizes and requires that seeds 0 and 1 compose exactly at this canonical index, with event size additive under posting.
Related “canonical” objects elsewhere in the library (Peano arithmetic, dyadic protocols, completed traces, self-similar dressings) play the same role of fixing a preferred representative; here the representative is simply the index 2.
proof idea
No proof. The declaration is the constant definition canonical_seed_post_index : ℕ := 2, justified by the doc-comment: seed levels 0 and 1 close at the next level.
why it matters
This constant is the glue point for the seed layer of the forcing chain. Downstream, canonicalSeedLevelEvent routes level 2 to the composite of levels 0 and 1 and leaves other levels as singleton supports; simp lemmas for levels 0, 1, 2 and the composition identity canonicalSeedLevelEvent_seed_composes all reduce through it.
The structure AdditiveSeedPostingModel and the constructor additive_seed_posting_model_of_recognition_work require that seeds 0 and 1 compose to the canonical seed level. admissibleOrbit_canonical_seed_size uses the index when stating that an admissible orbit supplies the canonical seed-size law via iteration of the framework map to this level.
In the T0–T8 narrative it is scaffolding for hierarchy forcing (ledger posting and discrete multilevel composition), not a direct proof of T5–T8, but without a fixed seed-post index the additive posting model cannot even be stated.
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