Pith Number

pith:XZUHKVVY

pith:2011:XZUHKVVYEB6T435XUIIQN3WWTK

not attested not anchored not stored refs pending

Upper and Lower Bounds for Kronecker Constants of Three-Element Sets of Integers

Kathryn E. Hare, L. Thomas Ramsey

arxiv:1108.3802 v2 · 2011-08-18 · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XZUHKVVYEB6T435XUIIQN3WWTK}

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	2026-05-18T04:15:05.117727Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

be687556b8207d3e6fb7a21106eed69a9585c291fadd99837412aa8e075cab2c

Aliases

arxiv: 1108.3802 · arxiv_version: 1108.3802v2 · doi: 10.48550/arxiv.1108.3802 · pith_short_12: XZUHKVVYEB6T · pith_short_16: XZUHKVVYEB6T435X · pith_short_8: XZUHKVVY

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/XZUHKVVYEB6T435XUIIQN3WWTK \
  | 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: be687556b8207d3e6fb7a21106eed69a9585c291fadd99837412aa8e075cab2c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "59370f6ad205cf23c2cf5fe3c506fb60c6b4264874f517695b2b7ac3b79708fb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2011-08-18T18:12:09Z",
    "title_canon_sha256": "da48c145fce36bf3adb0a57e4bc2cd546b6a51ef611257e0e49a21f08641d91c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.3802",
    "kind": "arxiv",
    "version": 2
  }
}