Pith Number

pith:ZWXWERWM

pith:2024:ZWXWERWMLXJ7ACLFDHZPH4JDXQ

not attested not anchored not stored refs pending

Homological $n$-systole in $(n+1)$-manifolds and bi-Ricci curvature

Jianchun Chu, Jintian Zhu, Man-Chun Lee

arxiv:2410.20785 v1 · 2024-10-28 · 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{ZWXWERWMLXJ7ACLFDHZPH4JDXQ}

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

A sharp spectral splitting theorem

Receipt and verification

First computed	2026-07-05T09:27:11.077621Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cdaf6246cc5dd3f0096519f2f3f123bc14b60712893329b784829e7817d18f81

Aliases

arxiv: 2410.20785 · arxiv_version: 2410.20785v1 · doi: 10.48550/arxiv.2410.20785 · pith_short_12: ZWXWERWMLXJ7 · pith_short_16: ZWXWERWMLXJ7ACLF · pith_short_8: ZWXWERWM

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/ZWXWERWMLXJ7ACLFDHZPH4JDXQ \
  | 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: cdaf6246cc5dd3f0096519f2f3f123bc14b60712893329b784829e7817d18f81

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e932d87ceb550d2ae09d1ab3a313b7263f22e551b259a7502080d426cebc764d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2024-10-28T07:02:08Z",
    "title_canon_sha256": "bcac36bad6ebf620193d465b2b505481643f17370540399fd229c5ecb2e26166"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2410.20785",
    "kind": "arxiv",
    "version": 1
  }
}