Pith Number

pith:XUVOIS4Z

pith:2018:XUVOIS4ZH3L5HAJ7LK6DDETWV5

not attested not anchored not stored refs pending

Sharp growth estimates for warping functions in multiply warped product manifolds

Bang-Yen Chen, Shihshu Walter Wei

arxiv:1809.05737 v1 · 2018-09-15 · math.DG · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XUVOIS4ZH3L5HAJ7LK6DDETWV5}

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	2026-05-18T00:05:36.672628Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bd2ae44b993ed7d3813f5abc319276af5609df4c30071ff12ccd95fbf99ae023

Aliases

arxiv: 1809.05737 · arxiv_version: 1809.05737v1 · doi: 10.48550/arxiv.1809.05737 · pith_short_12: XUVOIS4ZH3L5 · pith_short_16: XUVOIS4ZH3L5HAJ7 · pith_short_8: XUVOIS4Z

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/XUVOIS4ZH3L5HAJ7LK6DDETWV5 \
  | 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: bd2ae44b993ed7d3813f5abc319276af5609df4c30071ff12ccd95fbf99ae023

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8b37c008d924e6b302b290e01498a28972670de287913dccda177f377a17ce9a",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2018-09-15T16:12:38Z",
    "title_canon_sha256": "2fed59a215fda7b5e1026600b7b56eedcba32d99484e3a5f8a4d659f71c25ce1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1809.05737",
    "kind": "arxiv",
    "version": 1
  }
}