Pith Number

pith:ORQ6G5OD

pith:2026:ORQ6G5ODOISRF4TI7CFHJHJTMN

not attested not anchored not stored refs pending

A note on the second James-Hopf invariant

John R. Klein

arxiv:2606.29486 v1 · 2026-06-28 · 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{ORQ6G5ODOISRF4TI7CFHJHJTMN}

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	2026-06-30T01:18:08.682255Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7461e375c3722512f268f88a749d33634fec8f93a2e4d5e24e03dfcd0215dc92

Aliases

arxiv: 2606.29486 · arxiv_version: 2606.29486v1 · doi: 10.48550/arxiv.2606.29486 · pith_short_12: ORQ6G5ODOISR · pith_short_16: ORQ6G5ODOISRF4TI · pith_short_8: ORQ6G5OD

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/ORQ6G5ODOISRF4TI7CFHJHJTMN \
  | 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: 7461e375c3722512f268f88a749d33634fec8f93a2e4d5e24e03dfcd0215dc92

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "88d33286bb34b7c7b637520add4c3d1fc840554136876d82c18f9b752fa6bc58",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2026-06-28T16:36:26Z",
    "title_canon_sha256": "7d7c1eff1c128495461403a96ba8fd2851a611bc13487b08a78592e54a08adc2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.29486",
    "kind": "arxiv",
    "version": 1
  }
}