Pith Number

pith:OVLRWOFB

pith:2012:OVLRWOFBT3HL6TNPDPTSJIHBXQ

not attested not anchored not stored refs pending

Optimal observability of the multi-dimensional wave and Schr\"odinger equations in quantum ergodic domains

Emmanuel Tr\'elat, Enrique Zuazua, Yannick Privat

arxiv:1211.5655 v1 · 2012-11-24 · math.OC · math.AP · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OVLRWOFBT3HL6TNPDPTSJIHBXQ}

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	2026-05-18T03:40:02.331240Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

75571b38a19ecebf4daf1be724a0e1bc1fc1cb59e89253bd0555f7c22562fa59

Aliases

arxiv: 1211.5655 · arxiv_version: 1211.5655v1 · doi: 10.48550/arxiv.1211.5655 · pith_short_12: OVLRWOFBT3HL · pith_short_16: OVLRWOFBT3HL6TNP · pith_short_8: OVLRWOFB

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/OVLRWOFBT3HL6TNPDPTSJIHBXQ \
  | 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: 75571b38a19ecebf4daf1be724a0e1bc1fc1cb59e89253bd0555f7c22562fa59

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c7952b51347718b4ca28a8b06b6d3eb967ba36d2c7cdd9af94384fa7028a5981",
    "cross_cats_sorted": [
      "math.AP",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2012-11-24T10:04:07Z",
    "title_canon_sha256": "a66d161db290e0a40e1c168559f14373888ebadb866b45b5961cb7a9b7563832"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.5655",
    "kind": "arxiv",
    "version": 1
  }
}