Pith Number

pith:GNYVNMCD

pith:2010:GNYVNMCDW5EZ7ECYXVMFTIXVPG

not attested not anchored not stored refs pending

Invariant tori for the cubic Szeg\"o equation

Patrick G\'erard (LM-Orsay), Sandrine Grellier (MAPMO)

arxiv:1011.5479 v1 · 2010-11-24 · math.CV · 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{GNYVNMCDW5EZ7ECYXVMFTIXVPG}

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	2026-05-18T04:34:47.225301Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

337156b043b7499f9058bd5859a2f579a5a67dddf26e30907933af99f1fec8f2

Aliases

arxiv: 1011.5479 · arxiv_version: 1011.5479v1 · doi: 10.48550/arxiv.1011.5479 · pith_short_12: GNYVNMCDW5EZ · pith_short_16: GNYVNMCDW5EZ7ECY · pith_short_8: GNYVNMCD

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/GNYVNMCDW5EZ7ECYXVMFTIXVPG \
  | 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: 337156b043b7499f9058bd5859a2f579a5a67dddf26e30907933af99f1fec8f2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c5685f5e72b9bb3f3814e862b2e486fb7720fa0e5d56ce3c6ebf31888a4c8731",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2010-11-24T20:06:20Z",
    "title_canon_sha256": "ef183c0985c5b9e5a81fc18e3584bf767abd33b3da325ee11b19f8543880ca62"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.5479",
    "kind": "arxiv",
    "version": 1
  }
}