Pith Number

pith:7GJAQ5NM

pith:2000:7GJAQ5NMDOOUOFJHUO3ABFXSRB

not attested not anchored not stored refs pending

Oscillatory integral operators with low-order degeneracies

Allan Greenleaf, Andreas Seeger

arxiv:math/0007167 v3 · 2000-07-26 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7GJAQ5NMDOOUOFJHUO3ABFXSRB}

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	2026-07-04T14:34:37.042559Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f9920875ac1b9d471527a3b60096f2887305118b0981fbd5c45d96a2e44383c1

Aliases

arxiv: math/0007167 · arxiv_version: math/0007167v3 · doi: 10.48550/arxiv.math/0007167 · pith_short_12: 7GJAQ5NMDOOU · pith_short_16: 7GJAQ5NMDOOUOFJH · pith_short_8: 7GJAQ5NM

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/7GJAQ5NMDOOUOFJHUO3ABFXSRB \
  | 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: f9920875ac1b9d471527a3b60096f2887305118b0981fbd5c45d96a2e44383c1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1dd15e2263940ecfdffafe40c54c14feb7f5c66ec8759bdde0fe19e8bcd410e3",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.CA",
    "submitted_at": "2000-07-26T19:00:20Z",
    "title_canon_sha256": "4fe95c5acb88820075659435a07b73b2924b40b006b50b1ef2164fabd27cc1d7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0007167",
    "kind": "arxiv",
    "version": 3
  }
}