Pith Number

pith:PCYHKN7U

pith:2010:PCYHKN7UYN2LFORK7WFC6WKK7D

not attested not anchored not stored refs pending

The Gysin sequence for ${\mathbb S}^3$-actions on manifolds

J. I. Royo Prieto, Martintxo Saralegi-Aranguren (LML)

arxiv:1001.0388 v3 · 2010-01-03 · math.AG · 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{PCYHKN7UYN2LFORK7WFC6WKK7D}

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	2026-05-18T03:07:02.508862Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

78b07537f4c374b2ba2afd8a2f594af8ea5d871cf32173ac6c0d15ad19eb15dd

Aliases

arxiv: 1001.0388 · arxiv_version: 1001.0388v3 · doi: 10.48550/arxiv.1001.0388 · pith_short_12: PCYHKN7UYN2L · pith_short_16: PCYHKN7UYN2LFORK · pith_short_8: PCYHKN7U

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/PCYHKN7UYN2LFORK7WFC6WKK7D \
  | 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: 78b07537f4c374b2ba2afd8a2f594af8ea5d871cf32173ac6c0d15ad19eb15dd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "52d218179f9285535a2309e5a4153a12ee445544e62f2b48237f90c66d044704",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2010-01-03T16:47:50Z",
    "title_canon_sha256": "af037e6e1cc96e08e0f33571abf1b78f5d4ba998330838f964bafa4ab9254fcb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1001.0388",
    "kind": "arxiv",
    "version": 3
  }
}