Pith Number

pith:KNREIOOD

pith:2012:KNREIOODDZHLD6LDTCEZG7E7EY

not attested not anchored not stored refs pending

A congruence modulo four in real Schubert calculus

Frank Sottile, Igor zelenko, Nickolas Hein

arxiv:1211.7160 v3 · 2012-11-30 · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KNREIOODDZHLD6LDTCEZG7E7EY}

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	2026-05-18T03:05:54.898645Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

53624439c31e4eb1f9639889937c9f260bcc9fa83c6bd2de225c8e64afdc855d

Aliases

arxiv: 1211.7160 · arxiv_version: 1211.7160v3 · doi: 10.48550/arxiv.1211.7160 · pith_short_12: KNREIOODDZHL · pith_short_16: KNREIOODDZHLD6LD · pith_short_8: KNREIOOD

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/KNREIOODDZHLD6LDTCEZG7E7EY \
  | 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: 53624439c31e4eb1f9639889937c9f260bcc9fa83c6bd2de225c8e64afdc855d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3d0b8cd8e88fb8e04676e6b5f4667fa5688ed203d7b9202772d14c3739151f0d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2012-11-30T05:47:10Z",
    "title_canon_sha256": "b59bc8329e45588d6e67e0f8cae46ebb5fb2f7d54ddee78ccda5684cd212aed8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.7160",
    "kind": "arxiv",
    "version": 3
  }
}