Pith Number

pith:IYBNHPK5

pith:2012:IYBNHPK5IBTNEJAWERMW2WDTKI

not attested not anchored not stored refs pending

Spectral Theory of Partial Differential Equations - Lecture Notes

Richard S. Laugesen

arxiv:1203.2344 v1 · 2012-03-11 · math.AP · math-ph · 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{IYBNHPK5IBTNEJAWERMW2WDTKI}

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	2026-05-18T04:00:25.786062Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4602d3bd5d4066d2241624596d58735234ba2f8477189b9cb9563005c36f529b

Aliases

arxiv: 1203.2344 · arxiv_version: 1203.2344v1 · doi: 10.48550/arxiv.1203.2344 · pith_short_12: IYBNHPK5IBTN · pith_short_16: IYBNHPK5IBTNEJAW · pith_short_8: IYBNHPK5

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/IYBNHPK5IBTNEJAWERMW2WDTKI \
  | 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: 4602d3bd5d4066d2241624596d58735234ba2f8477189b9cb9563005c36f529b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7973738e5b5ce59700e63d88d8365930e75ca708fd2d8af91d9db53bb8e6b653",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-03-11T15:53:38Z",
    "title_canon_sha256": "cc9826f1823dd7ba344a8cca38e3be30df68b570aa3d1f8b71747a19940caf52"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.2344",
    "kind": "arxiv",
    "version": 1
  }
}