Pith Number

pith:57MZRY3U

pith:2003:57MZRY3UKSWWYSVHVLUCX4G7MW

not attested not anchored not stored refs pending

Closed symmetric monoidal structure and flow

Philippe Gaucher

arxiv:math/0308064 v1 · 2003-08-07 · math.AT · 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{57MZRY3UKSWWYSVHVLUCX4G7MW}

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	2026-05-18T01:05:28.740546Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

efd998e37454ad6c4aa7aae82bf0df65840a5d153f06117282c9db7732913248

Aliases

arxiv: math/0308064 · arxiv_version: math/0308064v1 · doi: 10.48550/arxiv.math/0308064 · pith_short_12: 57MZRY3UKSWW · pith_short_16: 57MZRY3UKSWWYSVH · pith_short_8: 57MZRY3U

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/57MZRY3UKSWWYSVHVLUCX4G7MW \
  | 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: efd998e37454ad6c4aa7aae82bf0df65840a5d153f06117282c9db7732913248

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d05bee19618385687fdb6955bc4c63d4e6270da45159697459d87dc832cc4f12",
    "cross_cats_sorted": [
      "math.CT"
    ],
    "license": "",
    "primary_cat": "math.AT",
    "submitted_at": "2003-08-07T10:11:12Z",
    "title_canon_sha256": "2268b2030b18a123b6195ed3a58c33d049fd22d905747c0e9f3391fae8cde9ac"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0308064",
    "kind": "arxiv",
    "version": 1
  }
}