Pith Number

pith:TSIFM5P7

pith:2015:TSIFM5P7L3PCD7NRRMRMNHWOKC

not attested not anchored not stored refs pending

Quantum ergodicity and quantum limits for sub-Riemannian Laplacians

Emmanuel Tr\'elat (LJLL), Luc Hillairet (MAPMO - FDP), Yves Colin de Verdi\`ere

arxiv:1505.01702 v2 · 2015-05-07 · math.SP · 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{TSIFM5P7L3PCD7NRRMRMNHWOKC}

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	2026-05-18T01:55:59.490328Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9c905675ff5ede21fdb18b22c69ece5082a4fbdcf39b723e7fe78bc9d910c8c3

Aliases

arxiv: 1505.01702 · arxiv_version: 1505.01702v2 · doi: 10.48550/arxiv.1505.01702 · pith_short_12: TSIFM5P7L3PC · pith_short_16: TSIFM5P7L3PCD7NR · pith_short_8: TSIFM5P7

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/TSIFM5P7L3PCD7NRRMRMNHWOKC \
  | 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: 9c905675ff5ede21fdb18b22c69ece5082a4fbdcf39b723e7fe78bc9d910c8c3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b54705c0d79c7fd4a359b34eb4e7c411d4a872726e2c8ba510ea7334cdffa0f4",
    "cross_cats_sorted": [
      "math-ph",
      "math.AP",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2015-05-07T13:46:32Z",
    "title_canon_sha256": "81e3c1400f1e312768c2fd7f624d333c2e698c9d293fe3a1248156063e169af4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.01702",
    "kind": "arxiv",
    "version": 2
  }
}