Pith Number

pith:BQ76Y2IV

pith:2015:BQ76Y2IVXL5WYPRP6IZTXNLWEC

not attested not anchored not stored refs pending

Complexity functions on 1-dimensional cohomology

Daryl Cooper, Stephan Tillmann

arxiv:1506.01793 v1 · 2015-06-05 · math.GT · math.DG · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BQ76Y2IVXL5WYPRP6IZTXNLWEC}

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	2026-05-18T01:55:59.216731Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0c3fec6915bafb6c3e2ff2333bb57620b5f600d46900ca37d0a24ae55851d78a

Aliases

arxiv: 1506.01793 · arxiv_version: 1506.01793v1 · doi: 10.48550/arxiv.1506.01793 · pith_short_12: BQ76Y2IVXL5W · pith_short_16: BQ76Y2IVXL5WYPRP · pith_short_8: BQ76Y2IV

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/BQ76Y2IVXL5WYPRP6IZTXNLWEC \
  | 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: 0c3fec6915bafb6c3e2ff2333bb57620b5f600d46900ca37d0a24ae55851d78a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "54194cc460e90c43402cd9338ddedc4fc7b3b22733518703c69c52d4c83106e7",
    "cross_cats_sorted": [
      "math.DG",
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2015-06-05T06:37:36Z",
    "title_canon_sha256": "7b7376fc6a738c4a3efca52369c1b39c8b414ea51d4301f364ca406431fbe860"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.01793",
    "kind": "arxiv",
    "version": 1
  }
}