Pith Number

pith:NT63D32G

pith:2012:NT63D32GBCG7AEU4MY2LJSGLMP

not attested not anchored not stored refs pending

On the classification of Killing submersions and their isometries

Jos\'e M. Manzano

arxiv:1211.2115 v1 · 2012-11-09 · 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{NT63D32GBCG7AEU4MY2LJSGLMP}

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	2026-05-18T02:33:01.597929Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6cfdb1ef46088df0129c6634b4c8cb63fb583ae56cd862a91c4b6839ec90ae26

Aliases

arxiv: 1211.2115 · arxiv_version: 1211.2115v1 · doi: 10.48550/arxiv.1211.2115 · pith_short_12: NT63D32GBCG7 · pith_short_16: NT63D32GBCG7AEU4 · pith_short_8: NT63D32G

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/NT63D32GBCG7AEU4MY2LJSGLMP \
  | 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: 6cfdb1ef46088df0129c6634b4c8cb63fb583ae56cd862a91c4b6839ec90ae26

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5ca0c3bbd14663c64ca67c387845092505279246be7be2f3ab68638956d00d5e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2012-11-09T12:51:24Z",
    "title_canon_sha256": "d47be7c2c5be95d87ba64dfdc2a5e0bcab4a26eb58d48c5eb5b03a425d494afc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.2115",
    "kind": "arxiv",
    "version": 1
  }
}