Pith Number

pith:K7AOBVOH

pith:2006:K7AOBVOH6SFMTIBFYUPA6PFWGP

not attested not anchored not stored refs pending

Self-Averaging Scaling Limits of Two-Frequency Wigner Distribution for Random Paraxial Waves

Albert C. Fannjiang

arxiv:physics/0609200 v4 · 2006-09-23 · physics.optics · physics.gen-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{K7AOBVOH6SFMTIBFYUPA6PFWGP}

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	2026-05-18T01:38:06.589638Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

57c0e0d5c7f48ac9a025c51e0f3cb633ff2ab06c61fc268b3880d60257fc0ec2

Aliases

arxiv: physics/0609200 · arxiv_version: physics/0609200v4 · doi: 10.48550/arxiv.physics/0609200 · pith_short_12: K7AOBVOH6SFM · pith_short_16: K7AOBVOH6SFMTIBF · pith_short_8: K7AOBVOH

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/K7AOBVOH6SFMTIBFYUPA6PFWGP \
  | 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: 57c0e0d5c7f48ac9a025c51e0f3cb633ff2ab06c61fc268b3880d60257fc0ec2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "07b61503afe9c567a3d09623617946adc88666addeefe1d91bc888257e185102",
    "cross_cats_sorted": [
      "physics.gen-ph"
    ],
    "license": "",
    "primary_cat": "physics.optics",
    "submitted_at": "2006-09-23T03:41:47Z",
    "title_canon_sha256": "8ad06f9a515fc0d9b6f517ea963fd68d0a073cdd37cca4e5b0343ef3c4434d9d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "physics/0609200",
    "kind": "arxiv",
    "version": 4
  }
}