Pith Number

pith:EY3X2YPR

pith:2019:EY3X2YPRK7G4S2OXSPSPXCY47I

not attested not anchored not stored refs pending

Strong Closed Range Estimates: Necessary Conditions and Applications

Andrew Raich, Phillip S. Harrington

arxiv:1904.09345 v1 · 2019-04-19 · math.CV

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{EY3X2YPRK7G4S2OXSPSPXCY47I}

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	2026-05-17T23:48:07.366600Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

26377d61f157cdc969d793e4fb8b1cfa2c778bff1258ed23dc0605ce374a7de6

Aliases

arxiv: 1904.09345 · arxiv_version: 1904.09345v1 · doi: 10.48550/arxiv.1904.09345 · pith_short_12: EY3X2YPRK7G4 · pith_short_16: EY3X2YPRK7G4S2OX · pith_short_8: EY3X2YPR

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/EY3X2YPRK7G4S2OXSPSPXCY47I \
  | 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: 26377d61f157cdc969d793e4fb8b1cfa2c778bff1258ed23dc0605ce374a7de6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "21367bd064b529f169a75c7102658c146adbe9ce8e12b4f30d09565e38ac4993",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2019-04-19T21:07:05Z",
    "title_canon_sha256": "884b555e66964e5040cef07bf40fec1cd957b042cf0ea33dd3c78022e279ee44"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1904.09345",
    "kind": "arxiv",
    "version": 1
  }
}