Pith Number

pith:CT3HNYQF

pith:2016:CT3HNYQF2YVXVB6NUYPMKYKDZY

not attested not anchored not stored refs pending

Spectral analysis of the Dirac operator on a 3-sphere

Dmitri Vassiliev, Michael Levitin, Yan-Long Fang

arxiv:1605.08589 v2 · 2016-05-27 · math.SP · gr-qc · math-ph · math.DG · 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{CT3HNYQF2YVXVB6NUYPMKYKDZY}

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	2026-05-18T00:08:31.658429Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

14f676e205d62b7a87cda61ec56143ce3be39e4164d0163cf2b4eefe372b4916

Aliases

arxiv: 1605.08589 · arxiv_version: 1605.08589v2 · doi: 10.48550/arxiv.1605.08589 · pith_short_12: CT3HNYQF2YVX · pith_short_16: CT3HNYQF2YVXVB6N · pith_short_8: CT3HNYQF

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/CT3HNYQF2YVXVB6NUYPMKYKDZY \
  | 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: 14f676e205d62b7a87cda61ec56143ce3be39e4164d0163cf2b4eefe372b4916

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "da395eddf967beebce2a673d72614b10a82b2d94d07b2d7b552660bd02ccba64",
    "cross_cats_sorted": [
      "gr-qc",
      "math-ph",
      "math.DG",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2016-05-27T11:34:12Z",
    "title_canon_sha256": "145520bc3960eaa377b65f0b3505dd386983822d0b503ddf6bf315c796aa9012"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1605.08589",
    "kind": "arxiv",
    "version": 2
  }
}