Pith Number

pith:CRGVP74P

pith:2026:CRGVP74P5HJDPE6YXRFGISFZDG

not attested not anchored not stored refs pending

Light Propagation through Space-Time Non-Markovian Random Media

Chaoran Wang, Chenjin Deng, Jinquan Qi, Shensheng Han, Shuang Liu

arxiv:2601.11213 v3 · 2026-01-16 · physics.optics · math-ph · math.MP · stat.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CRGVP74P5HJDPE6YXRFGISFZDG}

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	2026-08-04T01:58:40.380106Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

144d57ff8fe9d23793d8bc4a6448b9198736b09282557944373e19b05f06fd43

Aliases

arxiv: 2601.11213 · arxiv_version: 2601.11213v3 · doi: 10.48550/arxiv.2601.11213 · pith_short_12: CRGVP74P5HJD · pith_short_16: CRGVP74P5HJDPE6Y · pith_short_8: CRGVP74P

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/CRGVP74P5HJDPE6YXRFGISFZDG \
  | 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: 144d57ff8fe9d23793d8bc4a6448b9198736b09282557944373e19b05f06fd43

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "802d6d6a2aff109938d6053341106fc871d56f0fa1cce0f5621b3a54fd79df84",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "stat.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.optics",
    "submitted_at": "2026-01-16T11:40:21Z",
    "title_canon_sha256": "d5340909d74be3c9a8f937258158e24d63df49a4e40279b9de34e37c7cf1a173"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2601.11213",
    "kind": "arxiv",
    "version": 3
  }
}