Pith Number

pith:ND4ZEEGU

pith:2010:ND4ZEEGU3MHBDFHS2URIX7OSGI

not attested not anchored not stored refs pending

Spectral triples for hyperbolic dynamical systems

Michael F. Whittaker

arxiv:1011.3292 v2 · 2010-11-15 · math.OA · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ND4ZEEGU3MHBDFHS2URIX7OSGI}

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	2026-05-18T03:14:30.674919Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

68f99210d4db0e1194f2d5228bfdd23204d2618e9f61711ecd163c94ffab5d65

Aliases

arxiv: 1011.3292 · arxiv_version: 1011.3292v2 · doi: 10.48550/arxiv.1011.3292 · pith_short_12: ND4ZEEGU3MHB · pith_short_16: ND4ZEEGU3MHBDFHS · pith_short_8: ND4ZEEGU

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/ND4ZEEGU3MHBDFHS2URIX7OSGI \
  | 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: 68f99210d4db0e1194f2d5228bfdd23204d2618e9f61711ecd163c94ffab5d65

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "03e1eaed21b603dfc54a41f68ae53715a6fffc4b0d08048c8e1eae6c258767b6",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2010-11-15T05:18:40Z",
    "title_canon_sha256": "ced4d37ac7f6735d6ad40f48c7f52633eeb230d1bc259a236e9632c864fe4625"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.3292",
    "kind": "arxiv",
    "version": 2
  }
}