Pith Number

pith:ZEZ6H7KJ

pith:2015:ZEZ6H7KJJ3H6FXBRLM5MCML563

not attested not anchored not stored refs pending

Improved upper bounds for partial spreads

Sascha Kurz

arxiv:1512.04297 v2 · 2015-12-14 · math.CO · cs.DM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZEZ6H7KJJ3H6FXBRLM5MCML563}

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	2026-05-18T01:00:40.036885Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c933e3fd494ecfe2dc315b3ac1317df6dce36fe47a2c679b515344d76de58a2f

Aliases

arxiv: 1512.04297 · arxiv_version: 1512.04297v2 · doi: 10.48550/arxiv.1512.04297 · pith_short_12: ZEZ6H7KJJ3H6 · pith_short_16: ZEZ6H7KJJ3H6FXBR · pith_short_8: ZEZ6H7KJ

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/ZEZ6H7KJJ3H6FXBRLM5MCML563 \
  | 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: c933e3fd494ecfe2dc315b3ac1317df6dce36fe47a2c679b515344d76de58a2f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7069352a77e5bab39775f8fda30e122677e07b604a5cfbcb2424a3c51f401c60",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-12-14T13:11:38Z",
    "title_canon_sha256": "f3261543ff910f33138732882485404d79f19a96d0cf98a6644e531f9418dd54"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.04297",
    "kind": "arxiv",
    "version": 2
  }
}