Pith Number

pith:QYGACBGO

pith:2026:QYGACBGOKXFUVT5FRIIY4KNREW

not attested not anchored not stored refs resolved

Extended Abstract: Canonical join complex and cubical coordinates for all framing lattices

Cl\'ement Chenevi\`ere, Jonah Berggren

Bricks and brick cliques give a uniform combinatorial model for canonical join representations in every framing lattice.

arxiv:2605.15319 v1 · 2026-05-14 · math.CO

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\pithnumber{QYGACBGOKXFUVT5FRIIY4KNREW}

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Record completeness

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

We define bricks and brick cliques as a combinatorial model for join-irreducible elements and canonical join representations in all framing lattices, generalizing noncrossing arc diagrams, with a bijective proof and explicit reconstruction algorithm in two steps that also captures the natural bijection between join and meet representations and duality upon reflections.

C2weakest assumption

That the newly defined bricks and brick cliques correctly capture the join-irreducible elements and canonical join representations for every framing lattice, including those not previously studied with arc diagrams, so that the claimed bijective reconstruction works uniformly without additional restrictions on the framed graph.

C3one line summary

Defines bricks, brick cliques, and cubical coordinates for framing lattices with a bijective proof generalizing prior models for Tamari and weak orders.

References

6 extracted · 6 resolved · 0 Pith anchors

[1] The canonical complex of the weak order 2023

[2] Framing lattices and flow poly- topes 2024

[3] A unifying framework for the ν-Tamari lattice and principal order ideals in Young’s lattice 2023

[4] Kostant partitions functions and flow polytopes 2008

[5] Toric matrix Schubert varieties and their polytopes 2016

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:00:52.419893Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

860c0104ce55cb4acfa58a118e29b1258976298fb5cc20bd6676b462bea2d837

Aliases

arxiv: 2605.15319 · arxiv_version: 2605.15319v1 · doi: 10.48550/arxiv.2605.15319 · pith_short_12: QYGACBGOKXFU · pith_short_16: QYGACBGOKXFUVT5F · pith_short_8: QYGACBGO

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/QYGACBGOKXFUVT5FRIIY4KNREW \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 860c0104ce55cb4acfa58a118e29b1258976298fb5cc20bd6676b462bea2d837

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "71512266042ef09d011b6b4be65779b72906b70a43fb78f10c1cda5ae3f8af1a",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-sa/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-14T18:33:49Z",
    "title_canon_sha256": "a1a94257b22037e75709837bf25223735779549cabc68c496550cc1269834dce"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15319",
    "kind": "arxiv",
    "version": 1
  }
}