Pith Number

pith:C2Z6N5NF

pith:2012:C2Z6N5NFM5JFCFP4ZEKB2F6LOW

not attested not anchored not stored refs pending

Re-gauging groupoid, symmetries and degeneracies for Graph Hamiltonians and applications to the Gyroid wire network

Birgit Wehefritz-Kaufmann, Ralph M. Kaufmann, Sergei Khlebnikov

arxiv:1208.3266 v2 · 2012-08-16 · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{C2Z6N5NFM5JFCFP4ZEKB2F6LOW}

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	2026-05-18T00:43:18.966176Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

16b3e6f5a567525115fcc9141d17cb759749d9c578eb76a982fb417094751cd3

Aliases

arxiv: 1208.3266 · arxiv_version: 1208.3266v2 · doi: 10.48550/arxiv.1208.3266 · pith_short_12: C2Z6N5NFM5JF · pith_short_16: C2Z6N5NFM5JFCFP4 · pith_short_8: C2Z6N5NF

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/C2Z6N5NFM5JFCFP4ZEKB2F6LOW \
  | 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: 16b3e6f5a567525115fcc9141d17cb759749d9c578eb76a982fb417094751cd3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a9cd9b253d88afc5f585c6b06be2e391ae158d03c181cce41a2eb3b57fcbbd54",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2012-08-16T02:32:07Z",
    "title_canon_sha256": "3af059734ed327b325775b26e68707c89ded2da3e1427cfd37873df9dd3e8114"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.3266",
    "kind": "arxiv",
    "version": 2
  }
}