Pith Number

pith:5IJ57EJX

pith:2024:5IJ57EJXP2G5TADGZQ5YZ4KOHI

not attested not anchored not stored refs pending

Sharp bottom spectrum and scalar curvature rigidity

Bo Zhu, Jinmin Wang

arxiv:2408.08245 v4 · 2024-08-15 · math.DG · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5IJ57EJXP2G5TADGZQ5YZ4KOHI}

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	2026-06-19T16:09:46.641489Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ea13df91377e8dd98066cc3b8cf14e3a12c80c8d2f96af53bbeb4244741c4daa

Aliases

arxiv: 2408.08245 · arxiv_version: 2408.08245v4 · doi: 10.48550/arxiv.2408.08245 · pith_short_12: 5IJ57EJXP2G5 · pith_short_16: 5IJ57EJXP2G5TADG · pith_short_8: 5IJ57EJX

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/5IJ57EJXP2G5TADGZQ5YZ4KOHI \
  | 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: ea13df91377e8dd98066cc3b8cf14e3a12c80c8d2f96af53bbeb4244741c4daa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "789088e40d68fd39a244c03d983b3581eeba7a755741480e07007433f49276d2",
    "cross_cats_sorted": [
      "math.OA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2024-08-15T16:29:52Z",
    "title_canon_sha256": "1a65d2e565e1e9dd22f2948790fa3fc94d52d6cbd9cb59930a7d1b1e26ca58c6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2408.08245",
    "kind": "arxiv",
    "version": 4
  }
}