Pith Number

pith:OTARS4D2

pith:2015:OTARS4D26WNKO3E6UKNK2AHYXE

not attested not anchored not stored refs pending

Characterization of equality in Zhong-Yang type (sharp) spectral gap estimates for metric measure spaces

Sajjad Lakzian

arxiv:1506.04936 v2 · 2015-06-16 · 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{OTARS4D26WNKO3E6UKNK2AHYXE}

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	2026-05-17T23:55:43.504039Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

74c119707af59aa76c9ea29aad00f8b93e44d9026e4d87ab283e2f725f0cf457

Aliases

arxiv: 1506.04936 · arxiv_version: 1506.04936v2 · doi: 10.48550/arxiv.1506.04936 · pith_short_12: OTARS4D26WNK · pith_short_16: OTARS4D26WNKO3E6 · pith_short_8: OTARS4D2

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/OTARS4D26WNKO3E6UKNK2AHYXE \
  | 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: 74c119707af59aa76c9ea29aad00f8b93e44d9026e4d87ab283e2f725f0cf457

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a601b9c73a51a14ad35345b9154fbc550f0f184ab66649f0408bb8d2be68f05a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2015-06-16T12:20:42Z",
    "title_canon_sha256": "8758321aecf297660d25eefc8229c8de3ace66e139c00e6d2d3188732c59bc44"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.04936",
    "kind": "arxiv",
    "version": 2
  }
}