Pith Number

pith:GVHWGYQ5

pith:2018:GVHWGYQ5JHK4W4WPQ32I7QOUJN

not attested not anchored not stored refs pending

A corrected quantitative version of the Morse lemma

S\'ebastien Gou\"ezel, Vladimir Shchur

arxiv:1810.04579 v1 · 2018-10-10 · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GVHWGYQ5JHK4W4WPQ32I7QOUJN}

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	2026-05-18T00:03:39.690421Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

354f63621d49d5cb72cf86f48fc1d44b4870c0ecb72e364a26192f17a73bf1d3

Aliases

arxiv: 1810.04579 · arxiv_version: 1810.04579v1 · doi: 10.48550/arxiv.1810.04579 · pith_short_12: GVHWGYQ5JHK4 · pith_short_16: GVHWGYQ5JHK4W4WP · pith_short_8: GVHWGYQ5

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/GVHWGYQ5JHK4W4WPQ32I7QOUJN \
  | 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: 354f63621d49d5cb72cf86f48fc1d44b4870c0ecb72e364a26192f17a73bf1d3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e7c739b9e2ca650b704a4f34793be469de49b5378e1a969638ccd7f0b2cb6e87",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2018-10-10T15:07:46Z",
    "title_canon_sha256": "9f66ff8f66567921d5bf92718eda26fa170831117305a4bde242f851c6b8159f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1810.04579",
    "kind": "arxiv",
    "version": 1
  }
}