Pith Number

pith:2JQGBMQQ

pith:2026:2JQGBMQQGZEBCTGIOLJLW3DGS5

not attested not anchored not stored refs pending

Blow-ups of order types of positive density

Benedikt Hahn, Jes\'us Lea\~nos, Ruy Fabila-Monroy

arxiv:2606.07806 v1 · 2026-06-05 · math.CO · cs.CG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2JQGBMQQGZEBCTGIOLJLW3DGS5}

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	2026-06-09T01:04:52.680617Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d26060b2103648114cc872d2bb6c66975c11b46a0ae3390d783a010dfeb82741

Aliases

arxiv: 2606.07806 · arxiv_version: 2606.07806v1 · doi: 10.48550/arxiv.2606.07806 · pith_short_12: 2JQGBMQQGZEB · pith_short_16: 2JQGBMQQGZEBCTGI · pith_short_8: 2JQGBMQQ

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/2JQGBMQQGZEBCTGIOLJLW3DGS5 \
  | 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: d26060b2103648114cc872d2bb6c66975c11b46a0ae3390d783a010dfeb82741

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4117df68d4767249d6ef70d5a217480170cc4114eb445287839ef52f83fe9b43",
    "cross_cats_sorted": [
      "cs.CG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-05T19:34:47Z",
    "title_canon_sha256": "106d000962ef7093f7bb76574152ab549628c7315d0f8e6f89569221818662b9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.07806",
    "kind": "arxiv",
    "version": 1
  }
}