Pith Number

pith:OQ6COPJC

pith:2023:OQ6COPJCP7QTZ6KP72WQXYX2GL

not attested not anchored not stored refs pending

Slope inequality of fibered surfaces, Morsification conjecture and moduli of curves

Makoto Enokizono

arxiv:2307.04311 v3 · 2023-07-10 · 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{OQ6COPJCP7QTZ6KP72WQXYX2GL}

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.

Cited by

1 paper in Pith

Normal stable degenerations of Noether-Horikawa surfaces

Receipt and verification

First computed	2026-06-09T01:05:02.786253Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

743c273d227fe13cf94ffead0be2fa32cac4a0a71a898b760c5ecb56329b2fab

Aliases

arxiv: 2307.04311 · arxiv_version: 2307.04311v3 · doi: 10.48550/arxiv.2307.04311 · pith_short_12: OQ6COPJCP7QT · pith_short_16: OQ6COPJCP7QTZ6KP · pith_short_8: OQ6COPJC

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/OQ6COPJCP7QTZ6KP72WQXYX2GL \
  | 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: 743c273d227fe13cf94ffead0be2fa32cac4a0a71a898b760c5ecb56329b2fab

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4fb65e4fbb6681e6bdfb23c361a4f9ce363079307ffde6a82f8171e1a98dbf3d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2023-07-10T02:54:28Z",
    "title_canon_sha256": "190260be450c3d8d9811321b664ba90f3433b6decf9150afbf687429d2d05438"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2307.04311",
    "kind": "arxiv",
    "version": 3
  }
}