Pith Number

pith:647L7ZCH

pith:2011:647L7ZCHL7TTGCI4THM5KCBTHO

not attested not anchored not stored refs pending

The wave front set of oscillatory integrals with inhomogeneous phase function

Jochen Zahn

arxiv:1101.1861 v2 · 2011-01-10 · math.AP · 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{647L7ZCHL7TTGCI4THM5KCBTHO}

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	2026-05-18T04:26:54.518920Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f73ebfe4475fe733091c99d9d508333b8c63b87735483c077a9375ddfd43cf82

Aliases

arxiv: 1101.1861 · arxiv_version: 1101.1861v2 · doi: 10.48550/arxiv.1101.1861 · pith_short_12: 647L7ZCHL7TT · pith_short_16: 647L7ZCHL7TTGCI4 · pith_short_8: 647L7ZCH

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/647L7ZCHL7TTGCI4THM5KCBTHO \
  | 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: f73ebfe4475fe733091c99d9d508333b8c63b87735483c077a9375ddfd43cf82

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "715d19706089738b95c84c9fd11ada6bde74b66b8ca6d8565fb39874b5a28581",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-01-10T16:10:25Z",
    "title_canon_sha256": "7f1afb85184af96ad19f176a129b43ca78cc14d2d115cbb3b4d3c5f28dc354c2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.1861",
    "kind": "arxiv",
    "version": 2
  }
}