Pith Number

pith:X62BXTRJ

pith:2015:X62BXTRJWQDPAKBFH3XZBQUBSE

not attested not anchored not stored refs pending

String diagrams for traced and compact categories are oriented 1-cobordisms

David I. Spivak, Dylan Rupel, Patrick Schultz

arxiv:1508.01069 v3 · 2015-08-05 · 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{X62BXTRJWQDPAKBFH3XZBQUBSE}

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	2026-05-18T00:14:16.801928Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bfb41bce29b406f028253eef90c2819103dbc1139da5c4523e9c0100ffd4ffa9

Aliases

arxiv: 1508.01069 · arxiv_version: 1508.01069v3 · doi: 10.48550/arxiv.1508.01069 · pith_short_12: X62BXTRJWQDP · pith_short_16: X62BXTRJWQDPAKBF · pith_short_8: X62BXTRJ

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/X62BXTRJWQDPAKBFH3XZBQUBSE \
  | 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: bfb41bce29b406f028253eef90c2819103dbc1139da5c4523e9c0100ffd4ffa9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "299e652208f47a08fbfd1799d0c8516aa4fd5bb317915683bed7c2ebb4d50ad2",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2015-08-05T13:20:40Z",
    "title_canon_sha256": "3df69ca18d8adc8053ebbc01298a5a9c260af78e6ac02c7fb10906f639a345eb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.01069",
    "kind": "arxiv",
    "version": 3
  }
}