Pith Number

pith:TNMN77YL

pith:2026:TNMN77YLCVV7M7VHMG7CGISFLU

not attested not anchored not stored refs pending

Permutahedra, Lusztig varieties, degenerations, and subdivisions

Allen Knutson, Mario Sanchez, Melissa Sherman-Bennett

arxiv:2607.02701 v1 · 2026-07-02 · math.AG · math.CO

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TNMN77YLCVV7M7VHMG7CGISFLU}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

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.

Receipt and verification

First computed	2026-07-07T00:16:09.264634Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9b58dfff0b156bf67ea761be2322455d0f550c67aadd1ffff8c6d2aa3ae7f9bb

Aliases

arxiv: 2607.02701 · arxiv_version: 2607.02701v1 · doi: 10.48550/arxiv.2607.02701 · pith_short_12: TNMN77YLCVV7 · pith_short_16: TNMN77YLCVV7M7VH · pith_short_8: TNMN77YL

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/TNMN77YLCVV7M7VHMG7CGISFLU \
  | 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: 9b58dfff0b156bf67ea761be2322455d0f550c67aadd1ffff8c6d2aa3ae7f9bb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "04bc7a58498be726d0355caab75e63268580208ee171c7d183493d42cce389cb",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2026-07-02T18:43:57Z",
    "title_canon_sha256": "627309383141a304a44af38dae2e2715c5855e99fbbedbea926e9abf35e4562f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.02701",
    "kind": "arxiv",
    "version": 1
  }
}