Pith Number

pith:YG5RY3QA

pith:2009:YG5RY3QAVXNYT3XUSNUT4GTKWV

not attested not anchored not stored refs pending

Symplectic topology of Ma\~n\'e's critical values

G.P. Paternain, K. Cieliebak, U. Frauenfelder

arxiv:0903.0700 v4 · 2009-03-04 · math.SG · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YG5RY3QAVXNYT3XUSNUT4GTKWV}

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	2026-05-18T02:38:18.895149Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c1bb1c6e00addb89eef493693e1a6ab56c283ce20d294ef02fdae7fb59a5bf90

Aliases

arxiv: 0903.0700 · arxiv_version: 0903.0700v4 · doi: 10.48550/arxiv.0903.0700 · pith_short_12: YG5RY3QAVXNY · pith_short_16: YG5RY3QAVXNYT3XU · pith_short_8: YG5RY3QA

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/YG5RY3QAVXNYT3XUSNUT4GTKWV \
  | 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: c1bb1c6e00addb89eef493693e1a6ab56c283ce20d294ef02fdae7fb59a5bf90

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3978cdb8cc951b87f7d22a5f46c84993c9f7bd92f3dd96e5ea267d1ba27511b4",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SG",
    "submitted_at": "2009-03-04T06:50:08Z",
    "title_canon_sha256": "1c4bec5e7289fd1d07a70278d887385305da20ed9629660e4e09493f6fb356bf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0903.0700",
    "kind": "arxiv",
    "version": 4
  }
}