Pith Number

pith:VRI3GPZS

pith:2012:VRI3GPZSRMTW65FHIZOLKNK4V2

not attested not anchored not stored refs pending

Stable and Unstable operations in Algebraic Cobordism

Alexander Vishik

arxiv:1209.5793 v7 · 2012-09-25 · 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{VRI3GPZSRMTW65FHIZOLKNK4V2}

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	2026-05-18T00:30:50.945607Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ac51b33f328b276f74a7465cb5355cae9563bdab630843bc36e2127fa68b4d60

Aliases

arxiv: 1209.5793 · arxiv_version: 1209.5793v7 · doi: 10.48550/arxiv.1209.5793 · pith_short_12: VRI3GPZSRMTW · pith_short_16: VRI3GPZSRMTW65FH · pith_short_8: VRI3GPZS

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/VRI3GPZSRMTW65FHIZOLKNK4V2 \
  | 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: ac51b33f328b276f74a7465cb5355cae9563bdab630843bc36e2127fa68b4d60

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "09c39cad0328280a6f695a0dc35a6b68cc95ffd5b61ec039244e235728d780b1",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2012-09-25T23:35:02Z",
    "title_canon_sha256": "b7931fad5a7a73ef098a865972af8c9587866f5ac1a7814a5f175554cd693ba2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.5793",
    "kind": "arxiv",
    "version": 7
  }
}