Pith Number

pith:FS5XHQ6V

pith:2012:FS5XHQ6VJFI4XSN7772MAU3BX5

not attested not anchored not stored refs pending

Splitting vector bundles outside the stable range and A^1-homotopy sheaves of punctured affine spaces

Aravind Asok, Jean Fasel

arxiv:1209.5631 v4 · 2012-09-25 · math.AG · math.AC · math.AT · math.KT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FS5XHQ6VJFI4XSN7772MAU3BX5}

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	2026-05-18T02:49:54.598870Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2cbb73c3d54951cbc9bffff4c05361bf793423b7a84c6e67262174f9ffd22413

Aliases

arxiv: 1209.5631 · arxiv_version: 1209.5631v4 · doi: 10.48550/arxiv.1209.5631 · pith_short_12: FS5XHQ6VJFI4 · pith_short_16: FS5XHQ6VJFI4XSN7 · pith_short_8: FS5XHQ6V

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/FS5XHQ6VJFI4XSN7772MAU3BX5 \
  | 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: 2cbb73c3d54951cbc9bffff4c05361bf793423b7a84c6e67262174f9ffd22413

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8746f3cea09ae7a4d3f040278645bd406a9e90d6acea831787333d6eb67e05a7",
    "cross_cats_sorted": [
      "math.AC",
      "math.AT",
      "math.KT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2012-09-25T14:53:54Z",
    "title_canon_sha256": "eb8ecf0333f29765c816d94c7037e5a345e83c65746eae2f7d01994f098a7c28"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.5631",
    "kind": "arxiv",
    "version": 4
  }
}