Pith Number

pith:EE7FRGPB

pith:2016:EE7FRGPBBZFLKSUKLYHLXP66PQ

not attested not anchored not stored refs pending

Counting indices of critical points of rank two of polynomial selfmaps of R^4

Zbigniew Szafraniec

arxiv:1603.00666 v1 · 2016-03-02 · 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{EE7FRGPBBZFLKSUKLYHLXP66PQ}

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	2026-05-18T01:19:43.218889Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

213e5899e10e4ab54a8a5e0ebbbfde7c0bb0399b1bae5d21b5a1e0413f45c62f

Aliases

arxiv: 1603.00666 · arxiv_version: 1603.00666v1 · doi: 10.48550/arxiv.1603.00666 · pith_short_12: EE7FRGPBBZFL · pith_short_16: EE7FRGPBBZFLKSUK · pith_short_8: EE7FRGPB

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/EE7FRGPBBZFLKSUKLYHLXP66PQ \
  | 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: 213e5899e10e4ab54a8a5e0ebbbfde7c0bb0399b1bae5d21b5a1e0413f45c62f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c6b6e121b0488165d7302680e4c5e7877685650ad8bbbfbe5b376028c096dd02",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2016-03-02T11:53:20Z",
    "title_canon_sha256": "aa52e6b3f529da217a130f71a839a7302503a8c7f243a01d990afd2191567b25"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1603.00666",
    "kind": "arxiv",
    "version": 1
  }
}