Pith Number

pith:A4TPKIJZ

pith:2013:A4TPKIJZG5UWXSOSHHFKTYELJW

not attested not anchored not stored refs pending

Spectral asymmetry of the massless Dirac operator on a 3-torus

Dmitri Vassiliev, Michael Levitin, Robert J. Downes

arxiv:1306.5689 v2 · 2013-06-24 · math.SP · gr-qc · 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{A4TPKIJZG5UWXSOSHHFKTYELJW}

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	2026-05-18T03:07:34.105118Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0726f5213937696bc9d239caa9e08b4d8eb7bcbbbfaa4e0554a4e8f82969bf2f

Aliases

arxiv: 1306.5689 · arxiv_version: 1306.5689v2 · doi: 10.48550/arxiv.1306.5689 · pith_short_12: A4TPKIJZG5UW · pith_short_16: A4TPKIJZG5UWXSOS · pith_short_8: A4TPKIJZ

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/A4TPKIJZG5UWXSOSHHFKTYELJW \
  | 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: 0726f5213937696bc9d239caa9e08b4d8eb7bcbbbfaa4e0554a4e8f82969bf2f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7505fe88ca1e277e03d483866c496ea418e4f6bd731f8fbbc9a24b60454a1003",
    "cross_cats_sorted": [
      "gr-qc",
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2013-06-24T17:42:49Z",
    "title_canon_sha256": "240881b24e1123188979e1d9199ee1afa9fd7412c5e8be40a3ad47397693865a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.5689",
    "kind": "arxiv",
    "version": 2
  }
}