Pith Number

pith:N4W4KZFE

pith:2013:N4W4KZFEXW4CY3N5WHPSMM2NHF

not attested not anchored not stored refs pending

Fourier integrals and a new representation of Maslov's canonical operator near caustics

2), 2) ((1) A. Ishlinsky Institute for Problems in Mechanics, (2) Moscow Institute of Physics, (3) Department of Applied Mathematics, 4), (4) Institute of Applied, Computational Mathematics, Crete, Dolgoprudny, Foundation for Research, G. Makrakis (3, Greece, Greece), Heraklion, Moscow, Moscow District, Russia, S. Yu. Dobrokhotov (1, Technology, Technology-Hellas, University of Crete, V. E. Nazaikinskii (1

arxiv:1307.2292 v1 · 2013-07-08 · math-ph · math.AP · 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{N4W4KZFEXW4CY3N5WHPSMM2NHF}

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	2026-05-18T03:18:52.939843Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6f2dc564a4bdb82c6dbdb1df26334d395fdc898e93ea517d33f170fbe5e977d8

Aliases

arxiv: 1307.2292 · arxiv_version: 1307.2292v1 · doi: 10.48550/arxiv.1307.2292 · pith_short_12: N4W4KZFEXW4C · pith_short_16: N4W4KZFEXW4CY3N5 · pith_short_8: N4W4KZFE

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/N4W4KZFEXW4CY3N5WHPSMM2NHF \
  | 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: 6f2dc564a4bdb82c6dbdb1df26334d395fdc898e93ea517d33f170fbe5e977d8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d8ad56cae5b5562d3fc602676181c3bbe717db0d4fa1438e66159fdbb0035481",
    "cross_cats_sorted": [
      "math.AP",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2013-07-08T22:37:32Z",
    "title_canon_sha256": "9f99a7995951e5e72bfb98cff78e6fefa84c01034a1a227b556707d09cf36836"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.2292",
    "kind": "arxiv",
    "version": 1
  }
}