Pith Number

pith:6TA7RRRA

pith:2018:6TA7RRRAOXJXG75HV6QFCXWPZX

not attested not anchored not stored refs pending

Commutative cocycles and stable bundles over surfaces

Bernardo Villarreal, Daniel A. Ramras

arxiv:1807.03736 v3 · 2018-07-10 · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6TA7RRRAOXJXG75HV6QFCXWPZX}

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	2026-05-17T23:44:32.317870Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f4c1f8c62075d3737fa7afa0515ecfcde782d04c9d520ad7700b0c4cf4e27810

Aliases

arxiv: 1807.03736 · arxiv_version: 1807.03736v3 · doi: 10.48550/arxiv.1807.03736 · pith_short_12: 6TA7RRRAOXJX · pith_short_16: 6TA7RRRAOXJXG75H · pith_short_8: 6TA7RRRA

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/6TA7RRRAOXJXG75HV6QFCXWPZX \
  | 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: f4c1f8c62075d3737fa7afa0515ecfcde782d04c9d520ad7700b0c4cf4e27810

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "917cdf39a102eec901eef915569042dc5da84b192aa1df6ec66389497492a774",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2018-07-10T16:22:07Z",
    "title_canon_sha256": "8504ffcfac8449ee8a34cef40d8c6988c31e533ce680f1c4cf25493ecf984e91"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1807.03736",
    "kind": "arxiv",
    "version": 3
  }
}