Pith Number

pith:HPCOP3D7

pith:2021:HPCOP3D7L7EVD7JD5QTBL2PNHE

not attested not anchored not stored refs pending

Zero energy critical points of functionals depending on a parameter

Humberto Ramos Quoirin, Jefferson Silva, Kaye Silva

arxiv:2109.00930 v4 · 2021-09-02 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HPCOP3D7L7EVD7JD5QTBL2PNHE}

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	2026-07-05T03:43:04.773102Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3bc4e7ec7f5fc951fd23ec2615e9ed392d7ddcb781ac39106bbbb874e009ebf1

Aliases

arxiv: 2109.00930 · arxiv_version: 2109.00930v4 · doi: 10.48550/arxiv.2109.00930 · pith_short_12: HPCOP3D7L7EV · pith_short_16: HPCOP3D7L7EVD7JD · pith_short_8: HPCOP3D7

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/HPCOP3D7L7EVD7JD5QTBL2PNHE \
  | 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: 3bc4e7ec7f5fc951fd23ec2615e9ed392d7ddcb781ac39106bbbb874e009ebf1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "354c893d2697468aafafca36f487fbbab34029c2487e930706098cc1c2f91628",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2021-09-02T13:18:56Z",
    "title_canon_sha256": "7904f89b3fe3fe639a6081049ae71a051fb8f57f6c05e88a3470f29e5b056103"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2109.00930",
    "kind": "arxiv",
    "version": 4
  }
}