Pith Number

pith:THTEIZHD

pith:2013:THTEIZHDKHWTQTRXYS7UARGUZY

not attested not anchored not stored refs pending

Upper and lower bounds on $B_k^+$-sets

Craig Timmons

arxiv:1306.4941 v1 · 2013-06-20 · math.CO · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{THTEIZHDKHWTQTRXYS7UARGUZY}

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	2026-05-18T03:20:21.124994Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

99e64464e351ed384e37c4bf4044d4ce3e4b4a1f98c288a02414acf8f7e3d0b6

Aliases

arxiv: 1306.4941 · arxiv_version: 1306.4941v1 · doi: 10.48550/arxiv.1306.4941 · pith_short_12: THTEIZHDKHWT · pith_short_16: THTEIZHDKHWTQTRX · pith_short_8: THTEIZHD

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/THTEIZHDKHWTQTRXYS7UARGUZY \
  | 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: 99e64464e351ed384e37c4bf4044d4ce3e4b4a1f98c288a02414acf8f7e3d0b6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4ef537d38f95f92bb8fa5b5ffb78a946ed01ee4978117ae8e8735695237f7d3b",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-06-20T17:40:26Z",
    "title_canon_sha256": "6ccc70a8bd7c391c95e1c2e62b28b69ddf9aa191d24942956116b6666c2549b6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.4941",
    "kind": "arxiv",
    "version": 1
  }
}