Pith Number

pith:POA7OZRW

pith:2009:POA7OZRWVUED3YV3FQUQA4AF4H

not attested not anchored not stored refs pending

Entropy of semiclassical measures for nonpositively curved surfaces

Gabriel Riviere (CMLS-EcolePolytechnique)

arxiv:0911.1840 v1 · 2009-11-10 · math.DS · 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{POA7OZRWVUED3YV3FQUQA4AF4H}

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	2026-05-18T04:28:08.302892Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7b81f76636ad083de2bb2c29007005e1c37ee18a8d2e12bc5969a5c0e89a7153

Aliases

arxiv: 0911.1840 · arxiv_version: 0911.1840v1 · doi: 10.48550/arxiv.0911.1840 · pith_short_12: POA7OZRWVUED · pith_short_16: POA7OZRWVUED3YV3 · pith_short_8: POA7OZRW

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/POA7OZRWVUED3YV3FQUQA4AF4H \
  | 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: 7b81f76636ad083de2bb2c29007005e1c37ee18a8d2e12bc5969a5c0e89a7153

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "426f36ddf69e7ddb0af0cddb7065d17e4ce379af6c04bc93e773a63ce267701e",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2009-11-10T07:09:13Z",
    "title_canon_sha256": "beb487d1659d5bc3f9bb2311a61134e74f7f9f0327b79672ff81ba989cb9b789"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0911.1840",
    "kind": "arxiv",
    "version": 1
  }
}