Pith Number

pith:UN2NZQ5R

pith:2015:UN2NZQ5RZ6AL7R6LTPZPFE3N53

not attested not anchored not stored refs pending

Hopf measuring comonoids and enrichment

Christina Vasilakopoulou, Ignacio Lopez Franco, Martin Hyland

arxiv:1509.07632 v2 · 2015-09-25 · math.CT · math.QA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UN2NZQ5RZ6AL7R6LTPZPFE3N53}

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	2026-05-18T00:05:14.876193Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a374dcc3b1cf80bfc7cb9bf2f2936deee9dd7d32295cdf0e0160fc1d0f79f7ea

Aliases

arxiv: 1509.07632 · arxiv_version: 1509.07632v2 · doi: 10.48550/arxiv.1509.07632 · pith_short_12: UN2NZQ5RZ6AL · pith_short_16: UN2NZQ5RZ6AL7R6L · pith_short_8: UN2NZQ5R

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/UN2NZQ5RZ6AL7R6LTPZPFE3N53 \
  | 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: a374dcc3b1cf80bfc7cb9bf2f2936deee9dd7d32295cdf0e0160fc1d0f79f7ea

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "409717f0a523fe8ce534d9413cdcdb0a23a25a2530697e9d5f5ecf1e31b4aff7",
    "cross_cats_sorted": [
      "math.QA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2015-09-25T08:40:28Z",
    "title_canon_sha256": "a4ae8ad63da3cb0e54a4f1e79c27ef4599a2477f73532b07dc39c7d8def2a644"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.07632",
    "kind": "arxiv",
    "version": 2
  }
}