Pith Number

pith:XYTKJVZN

pith:2012:XYTKJVZN47S5JC5NIMTT3JAJBF

not attested not anchored not stored refs pending

Multi-scale discrete approximations of Fourier integral operators associated with canonical transformations and caustics

Andras Vasy, Gunther Uhlmann, Herwig Wendt, Maarten V. de Hoop

arxiv:1208.5416 v2 · 2012-08-27 · math.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XYTKJVZN47S5JC5NIMTT3JAJBF}

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	2026-05-18T02:03:38.561482Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

be26a4d72de7e5d48bad43273da409097f2a340fef864e1db4993f5d7f195540

Aliases

arxiv: 1208.5416 · arxiv_version: 1208.5416v2 · doi: 10.48550/arxiv.1208.5416 · pith_short_12: XYTKJVZN47S5 · pith_short_16: XYTKJVZN47S5JC5N · pith_short_8: XYTKJVZN

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/XYTKJVZN47S5JC5NIMTT3JAJBF \
  | 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: be26a4d72de7e5d48bad43273da409097f2a340fef864e1db4993f5d7f195540

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "12356d6490042bed7ff86f4e4c7f4f14bc6a9ea157c10fea7fa2ee3c527d04f9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2012-08-27T15:10:40Z",
    "title_canon_sha256": "198642d1f072560aed8b2fbd43dce7bddb309f90ff051372acf909ee1b01f33f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.5416",
    "kind": "arxiv",
    "version": 2
  }
}