Pith Number

pith:M7P6Z4YE

pith:2020:M7P6Z4YER54ABTIEWQNZPJUQRZ

not attested not anchored not stored refs pending

Comparison geometry of manifolds with boundary under lower $N$-weighted Ricci curvature bounds with $\varepsilon$-range

Kazuhiro Kuwae, Yohei Sakurai

arxiv:2011.03730 v1 · 2020-11-07 · 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{M7P6Z4YER54ABTIEWQNZPJUQRZ}

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	2026-07-05T01:49:58.587359Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

67dfecf3048f7800cd04b41b97a6908e410299ec32c8d47cd71a656b42aae1ed

Aliases

arxiv: 2011.03730 · arxiv_version: 2011.03730v1 · doi: 10.48550/arxiv.2011.03730 · pith_short_12: M7P6Z4YER54A · pith_short_16: M7P6Z4YER54ABTIE · pith_short_8: M7P6Z4YE

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/M7P6Z4YER54ABTIEWQNZPJUQRZ \
  | 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: 67dfecf3048f7800cd04b41b97a6908e410299ec32c8d47cd71a656b42aae1ed

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b69866d69ef3725124ff8e472235e8c865c3328371e6fd9b73ad54efc4a3df64",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2020-11-07T09:15:05Z",
    "title_canon_sha256": "abd00ccc1cf0d83c4034d6da995ed320f74c954095204fefa8a9113174500e02"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2011.03730",
    "kind": "arxiv",
    "version": 1
  }
}