Pith Number

pith:EDUNS7WK

pith:2011:EDUNS7WKXBDAAM3MUHWDCOMJHT

not attested not anchored not stored refs pending

A topologically induced 2-in/2-out operation on loop cohomology

Ronald Umble

arxiv:1108.5693 v9 · 2011-08-29 · 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{EDUNS7WKXBDAAM3MUHWDCOMJHT}

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	2026-05-18T03:55:35.560167Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

20e8d97ecab84600336ca1ec3139893ce0d12cab2ba4e432adad779fc373b0ea

Aliases

arxiv: 1108.5693 · arxiv_version: 1108.5693v9 · doi: 10.48550/arxiv.1108.5693 · pith_short_12: EDUNS7WKXBDA · pith_short_16: EDUNS7WKXBDAAM3M · pith_short_8: EDUNS7WK

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/EDUNS7WKXBDAAM3MUHWDCOMJHT \
  | 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: 20e8d97ecab84600336ca1ec3139893ce0d12cab2ba4e432adad779fc373b0ea

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "06aa1f45b2a36ab0c4861f3843fb7758d3f56262ae680295c1596c65fefc57fd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2011-08-29T18:29:10Z",
    "title_canon_sha256": "d598258c895f1131ee6b9aae48722dca655e89e7496c959271e58423422c9199"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.5693",
    "kind": "arxiv",
    "version": 9
  }
}