Pith Number

pith:F6SE34YP

pith:2011:F6SE34YPYA4UHQLHELDDTQP6J4

not attested not anchored not stored refs pending

Bohr-Sommerfeld phases for avoided crossings

Yves Colin De Verdi\`ere (IF)

arxiv:1103.1507 v1 · 2011-03-08 · 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{F6SE34YPYA4UHQLHELDDTQP6J4}

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	2026-05-18T04:27:15.711893Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2fa44df30fc03943c16722c639c1fe4f185dd90b0983d4171af326c76f0ccb7f

Aliases

arxiv: 1103.1507 · arxiv_version: 1103.1507v1 · doi: 10.48550/arxiv.1103.1507 · pith_short_12: F6SE34YPYA4U · pith_short_16: F6SE34YPYA4UHQLH · pith_short_8: F6SE34YP

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/F6SE34YPYA4UHQLHELDDTQP6J4 \
  | 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: 2fa44df30fc03943c16722c639c1fe4f185dd90b0983d4171af326c76f0ccb7f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6d5a7143fa3853e1f75a3e9dc3861bf26be20180b4a1329c9eb78e6c524a199e",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2011-03-08T12:40:37Z",
    "title_canon_sha256": "142caca3a21386d33b6d7e4e1360c29bda2a608c307608b15af468aeae9fd413"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.1507",
    "kind": "arxiv",
    "version": 1
  }
}