Pith Number

pith:2YUGDJDM

pith:2021:2YUGDJDMEJY6RCK35NG4SBEOON

not attested not anchored not stored refs pending

On the Maximal Number of Columns of a $\Delta$-modular Integer Matrix: Bounds and Computations

Gennadiy Averkov, Matthias Schymura

arxiv:2111.06294 v2 · 2021-11-11 · 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{2YUGDJDMEJY6RCK35NG4SBEOON}

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	2026-07-05T04:38:45.986032Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d62861a46c2271e8895beb4dc9048e73639f480148a62b1551bef8c3b3eb234b

Aliases

arxiv: 2111.06294 · arxiv_version: 2111.06294v2 · doi: 10.48550/arxiv.2111.06294 · pith_short_12: 2YUGDJDMEJY6 · pith_short_16: 2YUGDJDMEJY6RCK3 · pith_short_8: 2YUGDJDM

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/2YUGDJDMEJY6RCK35NG4SBEOON \
  | 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: d62861a46c2271e8895beb4dc9048e73639f480148a62b1551bef8c3b3eb234b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "55aa927c8fde5fe7077f46fe680ff4f3913d5762ec388245747eae8153b148f3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2021-11-11T16:13:24Z",
    "title_canon_sha256": "fdea15ae653dbeaf5ebc32a0ce9f5c904d502e28e77789ffd65083cb944c2fac"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2111.06294",
    "kind": "arxiv",
    "version": 2
  }
}