Pith Number

pith:GJP44MTP

pith:2015:GJP44MTP6VZMBPX4B77VKRMQ6F

not attested not anchored not stored refs pending

Universal Gysin formulas for flag bundles

Lionel Darondeau, Piotr Pragacz

arxiv:1510.07852 v4 · 2015-10-27 · 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{GJP44MTP6VZMBPX4B77VKRMQ6F}

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	2026-05-18T01:10:52.148546Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

325fce326ff572c0befc0fff554590f148425aab57918f30587f3966edce6800

Aliases

arxiv: 1510.07852 · arxiv_version: 1510.07852v4 · doi: 10.48550/arxiv.1510.07852 · pith_short_12: GJP44MTP6VZM · pith_short_16: GJP44MTP6VZMBPX4 · pith_short_8: GJP44MTP

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/GJP44MTP6VZMBPX4B77VKRMQ6F \
  | 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: 325fce326ff572c0befc0fff554590f148425aab57918f30587f3966edce6800

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2536717b4ebcaf2cb0f5c9e679d58e6d093c156552cf06ab9c8408c505c2a5d4",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2015-10-27T10:44:24Z",
    "title_canon_sha256": "a1961db5088513d67a2c15da361cb635256ff33c86ba0d1641ccc5798b1ac9d0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.07852",
    "kind": "arxiv",
    "version": 4
  }
}