Pith Number

pith:5BCCL3SD

pith:2015:5BCCL3SDLY3J2RF3ZHM3P745V3

not attested not anchored not stored refs pending

Spectral asymptotics for sub-Riemannian Laplacians. I: quantum ergodicity and quantum limits in the 3D contact case

Emmanuel Tr\'elat (LJLL), Luc Hillairet (MAPMO), Yves Colin De Verdi\`ere (IF)

arxiv:1504.07112 v4 · 2015-04-27 · math.SP · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5BCCL3SDLY3J2RF3ZHM3P745V3}

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	2026-05-18T00:23:02.137897Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e84425ee435e369d44bbc9d9b7ff9daefb3ff8a71049f5dd9f88abac408677a1

Aliases

arxiv: 1504.07112 · arxiv_version: 1504.07112v4 · doi: 10.48550/arxiv.1504.07112 · pith_short_12: 5BCCL3SDLY3J · pith_short_16: 5BCCL3SDLY3J2RF3 · pith_short_8: 5BCCL3SD

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/5BCCL3SDLY3J2RF3ZHM3P745V3 \
  | 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: e84425ee435e369d44bbc9d9b7ff9daefb3ff8a71049f5dd9f88abac408677a1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3ee79089e0f2723a896772384bad4f3ccdd226bc6693779fba9d74bf6959cc97",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2015-04-27T14:39:39Z",
    "title_canon_sha256": "37485ff441bdfd73da53170db6eb4c87392730ff98bdfd9331891b1d24d20055"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.07112",
    "kind": "arxiv",
    "version": 4
  }
}