Pith Number

pith:ZYH7U4W3

pith:2017:ZYH7U4W33F7UYRN63CQ6PP6WTI

not attested not anchored not stored refs pending

Upper and lower bounds for rich lines in grids

Brendan Murphy

arxiv:1709.10438 v2 · 2017-09-29 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZYH7U4W33F7UYRN63CQ6PP6WTI}

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

Some remarks on products of sets in the Heisenberg group and in the affine group

Receipt and verification

First computed	2026-05-18T00:01:47.427116Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ce0ffa72dbd97f4c45bed8a1e7bfd69a1a7bce021c3d1eb798819ef8f52911ec

Aliases

arxiv: 1709.10438 · arxiv_version: 1709.10438v2 · doi: 10.48550/arxiv.1709.10438 · pith_short_12: ZYH7U4W33F7U · pith_short_16: ZYH7U4W33F7UYRN6 · pith_short_8: ZYH7U4W3

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/ZYH7U4W33F7UYRN63CQ6PP6WTI \
  | 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: ce0ffa72dbd97f4c45bed8a1e7bfd69a1a7bce021c3d1eb798819ef8f52911ec

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b20e0cb1e31cc3934b9826db7f50d16ef3a3a87a467158494d98596bee918fd4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2017-09-29T14:52:16Z",
    "title_canon_sha256": "fdffd89088bcae5a7360b3a09abb74900b2f3c4072f479e73fd0dbea31285b3e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1709.10438",
    "kind": "arxiv",
    "version": 2
  }
}