Pith Number

pith:HCFM3YEA

pith:2012:HCFM3YEAL4KFFPBLLKFO663R2F

not attested not anchored not stored refs pending

On the multiplicity of solutions of a system of algebraic equations

Aleksandr Pukhlikov

arxiv:1205.1995 v1 · 2012-05-09 · 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{HCFM3YEAL4KFFPBLLKFO663R2F}

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	2026-05-18T03:55:58.029163Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

388acde0805f1452bc2b5a8aef7b71d1732fda156686473b2cc3fc320e68c6b5

Aliases

arxiv: 1205.1995 · arxiv_version: 1205.1995v1 · doi: 10.48550/arxiv.1205.1995 · pith_short_12: HCFM3YEAL4KF · pith_short_16: HCFM3YEAL4KFFPBL · pith_short_8: HCFM3YEA

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/HCFM3YEAL4KFFPBLLKFO663R2F \
  | 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: 388acde0805f1452bc2b5a8aef7b71d1732fda156686473b2cc3fc320e68c6b5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4c0ce1fffdde1153a08ad4eec50a51e675e3787b67fc92042c0eeae25e08e96c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2012-05-09T14:32:17Z",
    "title_canon_sha256": "e76fe7bc358d092ba988c35317c8b7f9ff457ed942483edd941f61738d5dcbd5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1205.1995",
    "kind": "arxiv",
    "version": 1
  }
}