Pith Number

pith:AP2YVIGU

pith:2011:AP2YVIGUPK6TMRC2RK44Y4GRBV

not attested not anchored not stored refs pending

On Hessian limit directions along non-oscillating gradient trajectories

Vincent Grandjean

arxiv:1103.0729 v1 · 2011-03-03 · math.CA · 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{AP2YVIGUPK6TMRC2RK44Y4GRBV}

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	2026-05-18T03:07:21.158100Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

03f58aa0d47abd36445a8ab9cc70d10d49a0ac9c8fcad22856f622d8bee8d93d

Aliases

arxiv: 1103.0729 · arxiv_version: 1103.0729v1 · doi: 10.48550/arxiv.1103.0729 · pith_short_12: AP2YVIGUPK6T · pith_short_16: AP2YVIGUPK6TMRC2 · pith_short_8: AP2YVIGU

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/AP2YVIGUPK6TMRC2RK44Y4GRBV \
  | 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: 03f58aa0d47abd36445a8ab9cc70d10d49a0ac9c8fcad22856f622d8bee8d93d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2cfa01f376ef7e4445506784a1a2ae3711b4b4497e00669627c34fed72e6bfa1",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2011-03-03T16:32:54Z",
    "title_canon_sha256": "84ca781c4617bb930c29d378963c92cb34f5b57fd80910a88b916298664ae908"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.0729",
    "kind": "arxiv",
    "version": 1
  }
}