Pith Number

pith:E5M533CS

pith:2016:E5M533CSTTDCECTRKHEM7HILVI

not attested not anchored not stored refs pending

Spectrally similar incommensurable 3-manifolds

Christian Millichap, David Futer

arxiv:1609.00748 v2 · 2016-09-02 · math.GT · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{E5M533CSTTDCECTRKHEM7HILVI}

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	2026-05-17T23:51:34.855309Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2759ddec529cc6220a7151c8cf9d0baa2e4e9c05f2f5d77136c51d3e841f70b1

Aliases

arxiv: 1609.00748 · arxiv_version: 1609.00748v2 · doi: 10.48550/arxiv.1609.00748 · pith_short_12: E5M533CSTTDC · pith_short_16: E5M533CSTTDCECTR · pith_short_8: E5M533CS

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/E5M533CSTTDCECTRKHEM7HILVI \
  | 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: 2759ddec529cc6220a7151c8cf9d0baa2e4e9c05f2f5d77136c51d3e841f70b1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a540c6ca136a11b05e5dcda5d735764e04a972108ffc31e94f1133a96c211044",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2016-09-02T21:03:30Z",
    "title_canon_sha256": "b62f1da284bab93e7d2c73ab6509813c5e5ee176390970af1d52640c531a3ee1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.00748",
    "kind": "arxiv",
    "version": 2
  }
}