Pith Number

pith:SCTQISEG

pith:2013:SCTQISEGNFRQBNJIGV2KVLQHZ5

not attested not anchored not stored refs pending

Two-cocycle twists and Atiyah-Patodi-Singer index theory

Charlotte Wahl, Sara Azzali

arxiv:1312.6373 v3 · 2013-12-22 · 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{SCTQISEGNFRQBNJIGV2KVLQHZ5}

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	2026-05-18T02:18:49.995791Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

90a7044886696300b5283574aaae07cf5af7d84c1cec1d52d7bc92025407414a

Aliases

arxiv: 1312.6373 · arxiv_version: 1312.6373v3 · doi: 10.48550/arxiv.1312.6373 · pith_short_12: SCTQISEGNFRQ · pith_short_16: SCTQISEGNFRQBNJI · pith_short_8: SCTQISEG

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/SCTQISEGNFRQBNJIGV2KVLQHZ5 \
  | 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: 90a7044886696300b5283574aaae07cf5af7d84c1cec1d52d7bc92025407414a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d29e4817f1e9a8cdab9f65328e897eb939df45b0503ca7725bb6ac8710ce4161",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2013-12-22T12:12:25Z",
    "title_canon_sha256": "068756af3173585dd0a744eff0976fc49c5d2c5970cd9b499afaac83d2274d28"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.6373",
    "kind": "arxiv",
    "version": 3
  }
}