Pith Number

pith:7WTUU3RL

pith:2016:7WTUU3RLK24HWMA4NSCSZNOBWX

not attested not anchored not stored refs pending

Observability properties of the homogeneous wave equation on a closed manifold

Emmanuel Humbert (LMPT), Emmanuel Tr\'elat (CaGE, LJLL), Yannick Privat (LJLL)

arxiv:1607.01535 v2 · 2016-07-06 · math.AP · math.DG · math.FA · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7WTUU3RLK24HWMA4NSCSZNOBWX}

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	2026-05-18T00:28:56.968476Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fda74a6e2b56b87b301c6c852cb5c1b5c0270b4eceade3c51b22d68e67c3cd97

Aliases

arxiv: 1607.01535 · arxiv_version: 1607.01535v2 · doi: 10.48550/arxiv.1607.01535 · pith_short_12: 7WTUU3RLK24H · pith_short_16: 7WTUU3RLK24HWMA4 · pith_short_8: 7WTUU3RL

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/7WTUU3RLK24HWMA4NSCSZNOBWX \
  | 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: fda74a6e2b56b87b301c6c852cb5c1b5c0270b4eceade3c51b22d68e67c3cd97

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8659a4b8a123fc4e4e552eb86199f9ad52a140b56b03f7409804a7909238dbac",
    "cross_cats_sorted": [
      "math.DG",
      "math.FA",
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-07-06T09:31:58Z",
    "title_canon_sha256": "7a1f296fd6d21331bf834b3bf3052817a76bc1eba0da1d0f733c4fd7b205dc91"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1607.01535",
    "kind": "arxiv",
    "version": 2
  }
}