Pith Number

pith:HT32RZXJ

pith:2026:HT32RZXJVLEP72UVTPNRSCHQVD

not attested not anchored not stored refs pending

On the Order-Conditional Optimality of Gaffke's Bound

Erik Learned-Miller, George Bissias

arxiv:2607.22971 v1 · 2026-07-25 · math.ST · cs.LG · math.PR · stat.ML · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HT32RZXJVLEP72UVTPNRSCHQVD}

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	2026-07-28T00:22:04.993067Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3cf7a8e6e9aac8ffea959bdb1908f0a8d6b57576b1b5db3a85e73dc2198c1c1e

Aliases

arxiv: 2607.22971 · arxiv_version: 2607.22971v1 · doi: 10.48550/arxiv.2607.22971 · pith_short_12: HT32RZXJVLEP · pith_short_16: HT32RZXJVLEP72UV · pith_short_8: HT32RZXJ

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/HT32RZXJVLEP72UVTPNRSCHQVD \
  | 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: 3cf7a8e6e9aac8ffea959bdb1908f0a8d6b57576b1b5db3a85e73dc2198c1c1e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "40d4e849bb72eb729c299da39607ffcf795216498c526169e1391e0c0866b858",
    "cross_cats_sorted": [
      "cs.LG",
      "math.PR",
      "stat.ML",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2026-07-25T00:40:52Z",
    "title_canon_sha256": "4c5059be99fcf4972b5bb31ad4b5fba067e38a7f2c4292dcccc0236468d2ae92"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.22971",
    "kind": "arxiv",
    "version": 1
  }
}