Pith Number

pith:TDCIELKZ

pith:2011:TDCIELKZRIJG7QJ7SD4MKXUVIK

not attested not anchored not stored refs pending

Generalized Dirac operators on Lorentzian manifolds and propagation of singularities

Paolo Antonini

arxiv:1110.1475 v1 · 2011-10-07 · math.DG · math-ph · math.AP · 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{TDCIELKZRIJG7QJ7SD4MKXUVIK}

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	2026-05-18T04:11:30.011467Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

98c4822d598a126fc13f90f8c55e9542af6e99bc9f7d2ec6ee16d1ce16b31701

Aliases

arxiv: 1110.1475 · arxiv_version: 1110.1475v1 · doi: 10.48550/arxiv.1110.1475 · pith_short_12: TDCIELKZRIJG · pith_short_16: TDCIELKZRIJG7QJ7 · pith_short_8: TDCIELKZ

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/TDCIELKZRIJG7QJ7SD4MKXUVIK \
  | 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: 98c4822d598a126fc13f90f8c55e9542af6e99bc9f7d2ec6ee16d1ce16b31701

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "986702c95350012c966ab36561c7c2df1b92ff7493680236ae211fcc6209fba3",
    "cross_cats_sorted": [
      "math-ph",
      "math.AP",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2011-10-07T10:17:37Z",
    "title_canon_sha256": "bb32d12e7a02bf5c219489aeb8c5ecb05c068c7b60500ad5be9f4bd0e47420bb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.1475",
    "kind": "arxiv",
    "version": 1
  }
}