Pith Number

pith:NFOYSF4I

pith:2012:NFOYSF4I6AVFO7H6TTQAUOIIKZ

not attested not anchored not stored refs pending

Location of the essential spectrum in curved quantum layers

David Krejcirik, Zhiqin Lu

arxiv:1211.2541 v1 · 2012-11-12 · math.DG · math-ph · math.FA · math.MP · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NFOYSF4I6AVFO7H6TTQAUOIIKZ}

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	2026-05-18T01:53:16.852683Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

695d891788f02a577cfe9ce00a3908565d4393f603515126c39b9aa63443c25f

Aliases

arxiv: 1211.2541 · arxiv_version: 1211.2541v1 · doi: 10.48550/arxiv.1211.2541 · pith_short_12: NFOYSF4I6AVF · pith_short_16: NFOYSF4I6AVFO7H6 · pith_short_8: NFOYSF4I

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/NFOYSF4I6AVFO7H6TTQAUOIIKZ \
  | 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: 695d891788f02a577cfe9ce00a3908565d4393f603515126c39b9aa63443c25f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "00b01819d7ffe55f5436796dc6b0a3ca3dd8fe93bb67911ad9f6c120d138c3c1",
    "cross_cats_sorted": [
      "math-ph",
      "math.FA",
      "math.MP",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2012-11-12T09:49:06Z",
    "title_canon_sha256": "f1339ae42a5c471b98073df39063496a3eddeb60d7bf4818f8cc677fd735dd91"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.2541",
    "kind": "arxiv",
    "version": 1
  }
}