Pith Number

pith:KPJPGQL2

pith:2012:KPJPGQL2QKC7J6YDE5HZ2JYQJ4

not attested not anchored not stored refs pending

Singularities, swallowtails and Dirac points. An analysis for families of Hamiltonians and applications to wire networks, especially the Gyroid

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

arxiv:1208.3262 v1 · 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{KPJPGQL2QKC7J6YDE5HZ2JYQJ4}

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	2026-05-18T03:47:00.564563Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

53d2f3417a8285f4fb03274f9d27104f3b8cd2418fcb275d4cd8b4e22ce1bf1e

Aliases

arxiv: 1208.3262 · arxiv_version: 1208.3262v1 · doi: 10.48550/arxiv.1208.3262 · pith_short_12: KPJPGQL2QKC7 · pith_short_16: KPJPGQL2QKC7J6YD · pith_short_8: KPJPGQL2

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/KPJPGQL2QKC7J6YDE5HZ2JYQJ4 \
  | 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: 53d2f3417a8285f4fb03274f9d27104f3b8cd2418fcb275d4cd8b4e22ce1bf1e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "feee120b9e36c20fe039bc5c028c7e48c82da76b3379693ae1bbaba3024f011f",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2012-08-16T01:48:31Z",
    "title_canon_sha256": "b71d14b1a9e983dbd6d67ffdadabff46547be85368a4a52a1c157dd17bc11dd3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.3262",
    "kind": "arxiv",
    "version": 1
  }
}