Pith Number

pith:XV2KE5LO

pith:2004:XV2KE5LOACF5VG722DAONNVCUT

not attested not anchored not stored refs pending

Crystals and coboundary categories

Andre Henriques, Joel Kamnitzer

arxiv:math/0406478 v3 · 2004-06-23 · math.QA · math.CO · math.CT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XV2KE5LOACF5VG722DAONNVCUT}

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.

Cited by

1 paper in Pith

Presentations for categories of crystals

Receipt and verification

First computed	2026-07-04T14:38:44.575823Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bd74a2756e008bda9bfad0c0e6b6a2a4cb3f2971133f60dda0830a5480ef61ff

Aliases

arxiv: math/0406478 · arxiv_version: math/0406478v3 · doi: 10.48550/arxiv.math/0406478 · pith_short_12: XV2KE5LOACF5 · pith_short_16: XV2KE5LOACF5VG72 · pith_short_8: XV2KE5LO

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/XV2KE5LOACF5VG722DAONNVCUT \
  | 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: bd74a2756e008bda9bfad0c0e6b6a2a4cb3f2971133f60dda0830a5480ef61ff

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d38c8ae3d7b6ade9f61726b48cfcc49ecbe87b876dd8091fb22fe5ca354a5ccf",
    "cross_cats_sorted": [
      "math.CO",
      "math.CT"
    ],
    "license": "",
    "primary_cat": "math.QA",
    "submitted_at": "2004-06-23T15:54:12Z",
    "title_canon_sha256": "1d5c23d5042c70a3f67b1b55c9f077923d4afa4e10c377dbac9ddc1e436bf476"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0406478",
    "kind": "arxiv",
    "version": 3
  }
}