Pith Number

pith:4Z5AHAVQ

pith:2013:4Z5AHAVQ6I4IRTKSILZCWBJYL5

not attested not anchored not stored refs pending

The symmetry of Spin^c Dirac spectrums on Riemannian product manifolds

Chanyoung Sung, Kyusik Hong

arxiv:1308.5279 v1 · 2013-08-24 · 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{4Z5AHAVQ6I4IRTKSILZCWBJYL5}

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	2026-05-18T03:15:07.212706Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e67a0382b0f23888cd5242f22b05385f66d4519f4d1b87f1b98cd550d750a971

Aliases

arxiv: 1308.5279 · arxiv_version: 1308.5279v1 · doi: 10.48550/arxiv.1308.5279 · pith_short_12: 4Z5AHAVQ6I4I · pith_short_16: 4Z5AHAVQ6I4IRTKS · pith_short_8: 4Z5AHAVQ

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/4Z5AHAVQ6I4IRTKSILZCWBJYL5 \
  | 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: e67a0382b0f23888cd5242f22b05385f66d4519f4d1b87f1b98cd550d750a971

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3f97f4a70e2b1a446211fcbf857818f82d63bc16d8916dc96bfd909544629554",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2013-08-24T01:55:28Z",
    "title_canon_sha256": "4d94c1edba4ae11f2146387deb2ab34cc0f3ccc5d0adb260a40a9cec790830b1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1308.5279",
    "kind": "arxiv",
    "version": 1
  }
}