Pith Number

pith:MRBZQAP4

pith:2015:MRBZQAP4OCLOB42W6O2MB4NFSL

not attested not anchored not stored refs pending

Rigidity of manifolds with boundary under a lower Bakry-E'mery Ricci curvature bound

Yohei Sakurai

arxiv:1506.03223 v4 · 2015-06-10 · 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{MRBZQAP4OCLOB42W6O2MB4NFSL}

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	2026-05-18T01:04:09.457029Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

64439801fc7096e0f356f3b4c0f1a592ec0053b31403e3bcb337915f2460aeb8

Aliases

arxiv: 1506.03223 · arxiv_version: 1506.03223v4 · doi: 10.48550/arxiv.1506.03223 · pith_short_12: MRBZQAP4OCLO · pith_short_16: MRBZQAP4OCLOB42W · pith_short_8: MRBZQAP4

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/MRBZQAP4OCLOB42W6O2MB4NFSL \
  | 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: 64439801fc7096e0f356f3b4c0f1a592ec0053b31403e3bcb337915f2460aeb8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0b842d2a56a16cf93979294f4a4e5979f97acf1ffe37d9e51a895ffcb61540ee",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2015-06-10T09:09:35Z",
    "title_canon_sha256": "8ae8931449dc2065576f4b00e830fd282acc6706423232cb8eb7a9faa8aa9373"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.03223",
    "kind": "arxiv",
    "version": 4
  }
}