Pith Number

pith:VUWIVZ2Q

pith:2010:VUWIVZ2QPQ6WIAMDAEXD2H7PIG

not attested not anchored not stored refs pending

Associahedra and Weak Monoidal Structures on Categories

Rainer M. Vogt, Steven Gubkin, Zbigniew Fiedorowicz

arxiv:1005.3979 v4 · 2010-05-21 · math.AT · 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{VUWIVZ2QPQ6WIAMDAEXD2H7PIG}

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	2026-05-18T02:25:19.257120Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ad2c8ae7507c3d640183012e3d1fef41ac62bc86d3918645ef464c4a193652c8

Aliases

arxiv: 1005.3979 · arxiv_version: 1005.3979v4 · doi: 10.48550/arxiv.1005.3979 · pith_short_12: VUWIVZ2QPQ6W · pith_short_16: VUWIVZ2QPQ6WIAMD · pith_short_8: VUWIVZ2Q

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/VUWIVZ2QPQ6WIAMDAEXD2H7PIG \
  | 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: ad2c8ae7507c3d640183012e3d1fef41ac62bc86d3918645ef464c4a193652c8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2fe0665b528490789ad873ee781e5293f24f57d0d6a5e668743cc913cbd015e1",
    "cross_cats_sorted": [
      "math.CO",
      "math.CT"
    ],
    "license": "http://creativecommons.org/licenses/by/3.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2010-05-21T15:15:47Z",
    "title_canon_sha256": "d60126651c4c47312f0c809f323102c5c89a9e03ae8554e38fbf510f0d246066"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1005.3979",
    "kind": "arxiv",
    "version": 4
  }
}