Pith Number

pith:KCRAZXBK

pith:2026:KCRAZXBKWOBCKRCAYT7JH77VYL

not attested not anchored not stored refs pending

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

Jiaping Wang, Ovidiu Munteanu

arxiv:2607.06508 v1 · 2026-07-07 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KCRAZXBKWOBCKRCAYT7JH77VYL}

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

McKean Rigidity for Cocompact Negatively Curved Manifolds and the \(p\)-Laplacian

Receipt and verification

First computed	2026-07-08T01:19:28.371817Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

50a20cdc2ab382254440c4fe93fff5c2d435cf5c163a6865d0bb6820a4eccb11

Aliases

arxiv: 2607.06508 · arxiv_version: 2607.06508v1 · doi: 10.48550/arxiv.2607.06508 · pith_short_12: KCRAZXBKWOBC · pith_short_16: KCRAZXBKWOBCKRCA · pith_short_8: KCRAZXBK

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/KCRAZXBKWOBCKRCAYT7JH77VYL \
  | 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: 50a20cdc2ab382254440c4fe93fff5c2d435cf5c163a6865d0bb6820a4eccb11

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b910ba917b8fafec2d5b92b201548eaae7c6a3f54de0947dcc1f636add4c1bed",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2026-07-07T17:11:54Z",
    "title_canon_sha256": "ce4770b88137526ab5c5b7643652f74892d42e6edc06a65d924a490e0a0d41f8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.06508",
    "kind": "arxiv",
    "version": 1
  }
}