Pith Number

pith:JMKJNAYC

pith:2026:JMKJNAYC6YBVRMNNZ7JTZUENZI

not attested not anchored not stored refs pending

Space-Entropy Lower Bounds for Random Sampling

Feras A. Saad, Thomas L. Draper

arxiv:2607.14503 v1 · 2026-07-16 · cs.CC · cs.DS · cs.IT · math.IT · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JMKJNAYC6YBVRMNNZ7JTZUENZI}

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	2026-07-17T00:21:15.808480Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4b14968302f60358b1adcfd33cd08dca0b4fc458b4de520816ccc8f6939a52e1

Aliases

arxiv: 2607.14503 · arxiv_version: 2607.14503v1 · doi: 10.48550/arxiv.2607.14503 · pith_short_12: JMKJNAYC6YBV · pith_short_16: JMKJNAYC6YBVRMNN · pith_short_8: JMKJNAYC

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/JMKJNAYC6YBVRMNNZ7JTZUENZI \
  | 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: 4b14968302f60358b1adcfd33cd08dca0b4fc458b4de520816ccc8f6939a52e1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ee6e3c84d21e5182258a3d175c2f0bd534aa71161ed6a331d74d0030a987d48c",
    "cross_cats_sorted": [
      "cs.DS",
      "cs.IT",
      "math.IT",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CC",
    "submitted_at": "2026-07-16T02:37:38Z",
    "title_canon_sha256": "d42b308087200bde465f1b44bfa18c6b4b2193622695f2be4215d1b2849f7e63"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.14503",
    "kind": "arxiv",
    "version": 1
  }
}