Pith Number

pith:3APCTDA3

pith:2023:3APCTDA3UXU7ZO3OKC4FKB54Z3

not attested not anchored not stored refs pending

A Useful Inequality for the Binary Entropy Function

Ravi B. Boppana (MIT)

arxiv:2301.09664 v1 · 2023-01-23 · math.CO · cs.CC · cs.IT · math.IT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3APCTDA3UXU7ZO3OKC4FKB54Z3}

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.

Cited by

1 paper in Pith

Redundancy Is All You Need (for CSP Sparsification)

Receipt and verification

First computed	2026-07-05T05:35:04.511235Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d81e298c1ba5e9fcbb6e50b85507bcceea36f882c85b5dbb9093447c7c4504e5

Aliases

arxiv: 2301.09664 · arxiv_version: 2301.09664v1 · doi: 10.48550/arxiv.2301.09664 · pith_short_12: 3APCTDA3UXU7 · pith_short_16: 3APCTDA3UXU7ZO3O · pith_short_8: 3APCTDA3

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/3APCTDA3UXU7ZO3OKC4FKB54Z3 \
  | 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: d81e298c1ba5e9fcbb6e50b85507bcceea36f882c85b5dbb9093447c7c4504e5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "11d6f04a2d48e881e8d2814f599000e87f8aab6bb39ecff2da6565d4c08ac0fd",
    "cross_cats_sorted": [
      "cs.CC",
      "cs.IT",
      "math.IT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2023-01-23T19:02:37Z",
    "title_canon_sha256": "ffbd0020d134cac6688ed1c5351e3ad4e75005daf16caebeba4e281b4daa0522"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2301.09664",
    "kind": "arxiv",
    "version": 1
  }
}