Pith Number

pith:FXR4XKGP

pith:2012:FXR4XKGP3OJ6D2NCGJOK3LRPKG

not attested not anchored not stored refs pending

Kirchhoff's theorems in higher dimensions and Reidemeister torsion

John R. Klein, Michael J. Catanzaro, Vladimir Y. Chernyak

arxiv:1206.6783 v2 · 2012-06-28 · 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{FXR4XKGP3OJ6D2NCGJOK3LRPKG}

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	2026-05-18T03:51:13.812907Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2de3cba8cfdb93e1e9a2325cadae2f518435467041ecb9a48ee612ed7ab1ac86

Aliases

arxiv: 1206.6783 · arxiv_version: 1206.6783v2 · doi: 10.48550/arxiv.1206.6783 · pith_short_12: FXR4XKGP3OJ6 · pith_short_16: FXR4XKGP3OJ6D2NC · pith_short_8: FXR4XKGP

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/FXR4XKGP3OJ6D2NCGJOK3LRPKG \
  | 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: 2de3cba8cfdb93e1e9a2325cadae2f518435467041ecb9a48ee612ed7ab1ac86

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "97aa1d69daaa37b77575d4faf560b44d0edc0f27811629df1520b5dd450d7687",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2012-06-28T18:05:59Z",
    "title_canon_sha256": "88f32449ca7a69606a4569f9f9d208715a876a44aaa14b5f61b3c43def73023e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.6783",
    "kind": "arxiv",
    "version": 2
  }
}