Pith Number

pith:GYSP4QE7

pith:2009:GYSP4QE7WKWP2JTH2OTKSK65LI

not attested not anchored not stored refs pending

Geometry of expanding absolutely continuous invariant measures and the liftability problem

Carla L. Dias, Jose F. Alves, Stefano Luzzatto

arxiv:0910.2547 v3 · 2009-10-14 · math.DS

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

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	2026-05-18T03:41:30.977518Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3624fe409fb2acfd2667d3a6a92bdd5a3f476459dc18f9cbc11b569c24ef4c1b

Aliases

arxiv: 0910.2547 · arxiv_version: 0910.2547v3 · doi: 10.48550/arxiv.0910.2547 · pith_short_12: GYSP4QE7WKWP · pith_short_16: GYSP4QE7WKWP2JTH · pith_short_8: GYSP4QE7

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/GYSP4QE7WKWP2JTH2OTKSK65LI \
  | 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: 3624fe409fb2acfd2667d3a6a92bdd5a3f476459dc18f9cbc11b569c24ef4c1b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "88b04bb675165ed7d0ac024742c2729fe5165ae557836f2e8d8d2c4f263f6d54",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2009-10-14T08:12:03Z",
    "title_canon_sha256": "e9b0c86dc34776ad77ef95cd24b2711c62ba3b6204a287d98f84fa039c3b1e1e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0910.2547",
    "kind": "arxiv",
    "version": 3
  }
}