Pith Number

pith:OK4PLHYS

pith:2024:OK4PLHYSSM3LMWNRV2VJI2RDBF

not attested not anchored not stored refs pending

A sharp spectral splitting theorem

Gioacchino Antonelli, Kai Xu, Marco Pozzetta

arxiv:2412.12707 v1 · 2024-12-17 · math.DG · math.AP

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OK4PLHYSSM3LMWNRV2VJI2RDBF}

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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

8 papers in Pith

Bottom spectrum and parabolicity of 3-manifolds with scalar curvature lower bound

Band Width Estimates and Rigidity of Manifolds with Negative Curvature

Spectral splitting theorem and ends of minimal hypersurfaces

Criticality, splitting theorems under spectral Ricci bounds and the topology of stable minimal hypersurfaces

Receipt and verification

First computed	2026-07-05T09:50:19.559766Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

72b8f59f129336b659b1aeaa946a23096ba76101c7bb9afba5cd4583d50b7612

Aliases

arxiv: 2412.12707 · arxiv_version: 2412.12707v1 · doi: 10.48550/arxiv.2412.12707 · pith_short_12: OK4PLHYSSM3L · pith_short_16: OK4PLHYSSM3LMWNR · pith_short_8: OK4PLHYS

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/OK4PLHYSSM3LMWNRV2VJI2RDBF \
  | 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: 72b8f59f129336b659b1aeaa946a23096ba76101c7bb9afba5cd4583d50b7612

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ab8b0095f65ada009baa67b88013935bf2d49ae257beba4a1896c569f0df6b2b",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2024-12-17T09:20:55Z",
    "title_canon_sha256": "a82247e9021727dabbff04080f23992a3c5d5fec8d9da7bcb1f1afc1ed1cdb19"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.12707",
    "kind": "arxiv",
    "version": 1
  }
}