Pith Number

pith:NWISSMRA

pith:2012:NWISSMRA52J2MBF6PYBTVFRECV

not attested not anchored not stored refs pending

On Kirchhoff's theorems with coefficients in a line bundle

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

arxiv:1207.2822 v2 · 2012-07-12 · math.AT · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NWISSMRA52J2MBF6PYBTVFRECV}

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	2026-05-18T03:21:31.740170Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6d91293220ee93a604be7e033a96241540d4355199b8536f5c98672fe25ad85f

Aliases

arxiv: 1207.2822 · arxiv_version: 1207.2822v2 · doi: 10.48550/arxiv.1207.2822 · pith_short_12: NWISSMRA52J2 · pith_short_16: NWISSMRA52J2MBF6 · pith_short_8: NWISSMRA

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/NWISSMRA52J2MBF6PYBTVFRECV \
  | 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: 6d91293220ee93a604be7e033a96241540d4355199b8536f5c98672fe25ad85f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d53a70c8c8a3c41c1bdf60ce5c7734bf0fcbd255ea6d444b16fcee485428c154",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2012-07-12T01:39:06Z",
    "title_canon_sha256": "98911a365c9e7b45919824c68bd32f568afed85655629112b12b67ab38343fcb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.2822",
    "kind": "arxiv",
    "version": 2
  }
}