Pith Number

pith:LM63ZMNK

pith:2013:LM63ZMNKLEIE67QHWAUW2PFXSL

not attested not anchored not stored refs pending

The Eigenvector Moment Flow and local Quantum Unique Ergodicity

Horng-Tzer Yau, Paul Bourgade

arxiv:1312.1301 v6 · 2013-12-04 · math.PR · 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{LM63ZMNKLEIE67QHWAUW2PFXSL}

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	2026-05-18T01:23:09.070464Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5b3dbcb1aa59104f7e07b0296d3cb792d25b11519bb5e1fc77872c35866f58ab

Aliases

arxiv: 1312.1301 · arxiv_version: 1312.1301v6 · doi: 10.48550/arxiv.1312.1301 · pith_short_12: LM63ZMNKLEIE · pith_short_16: LM63ZMNKLEIE67QH · pith_short_8: LM63ZMNK

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/LM63ZMNKLEIE67QHWAUW2PFXSL \
  | 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: 5b3dbcb1aa59104f7e07b0296d3cb792d25b11519bb5e1fc77872c35866f58ab

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "55a3ebe11bc4be3198af90411c68cc4deb59e103e81148c4f01cae41eed8c98a",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-12-04T19:51:51Z",
    "title_canon_sha256": "2ceb306c11ed455d5c7d92a9c63094ea588f8931ebab50cc1a1df720f0701aa8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.1301",
    "kind": "arxiv",
    "version": 6
  }
}