Pith Number

pith:KV5JIXN6

pith:2010:KV5JIXN6S3FHQMKM6S5XDAJ23H

not attested not anchored not stored refs pending

Spectral triples and Gibbs measures for expanding maps on Cantor sets

Richard Sharp

arxiv:1009.5887 v1 · 2010-09-29 · math.DS · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KV5JIXN6S3FHQMKM6S5XDAJ23H}

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	2026-05-18T04:40:08.673970Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

557a945dbe96ca78314cf4bb71813ad9f3e847c57f1a7b0fec3fe46dfda1da76

Aliases

arxiv: 1009.5887 · arxiv_version: 1009.5887v1 · doi: 10.48550/arxiv.1009.5887 · pith_short_12: KV5JIXN6S3FH · pith_short_16: KV5JIXN6S3FHQMKM · pith_short_8: KV5JIXN6

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/KV5JIXN6S3FHQMKM6S5XDAJ23H \
  | 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: 557a945dbe96ca78314cf4bb71813ad9f3e847c57f1a7b0fec3fe46dfda1da76

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "af07d2926a4288084d6e56507e6843f1e866b1770c7bdb0727b5644c0a09c50c",
    "cross_cats_sorted": [
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2010-09-29T14:08:50Z",
    "title_canon_sha256": "aeb95264cd90b3e5bc9853a38c51b962c77d8140cc77860281bc5013bb2f1fa9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.5887",
    "kind": "arxiv",
    "version": 1
  }
}