Pith Number

pith:XA4UBSZW

pith:2015:XA4UBSZWJPSE4AFOJI5EU33EDK

not attested not anchored not stored refs pending

Affine Hopf fibration

S. Tabachnikov, V. Ovsienko

arxiv:1511.08894 v2 · 2015-11-28 · math.AT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XA4UBSZWJPSE4AFOJI5EU33EDK}

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	2026-05-18T01:25:33.083798Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b83940cb364be44e00ae4a3a4a6f641a90479b8f7f716a446cbe2376c3af4def

Aliases

arxiv: 1511.08894 · arxiv_version: 1511.08894v2 · doi: 10.48550/arxiv.1511.08894 · pith_short_12: XA4UBSZWJPSE · pith_short_16: XA4UBSZWJPSE4AFO · pith_short_8: XA4UBSZW

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/XA4UBSZWJPSE4AFOJI5EU33EDK \
  | 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: b83940cb364be44e00ae4a3a4a6f641a90479b8f7f716a446cbe2376c3af4def

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "29dfef773ee1e10c54685fe7524b17699c94f1fe6bfd98a6523c8076801b1ec7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2015-11-28T12:54:11Z",
    "title_canon_sha256": "55467c37bc6a53f5fdc8c982ab6577acaf69c8a52796d507afda454f21500307"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.08894",
    "kind": "arxiv",
    "version": 2
  }
}