Pith Number

pith:QLZDF5VT

pith:2018:QLZDF5VTEZZ5LCDVHBGPSXBWNK

not attested not anchored not stored refs pending

New lower bound on the Shannon capacity of C7 from circular graphs

Alexander Schrijver, Sven Polak

arxiv:1808.07438 v2 · 2018-08-22 · math.CO · cs.IT · math.IT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QLZDF5VTEZZ5LCDVHBGPSXBWNK}

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	2026-05-17T23:43:43.131596Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

82f232f6b32673d58875384cf95c366ab10e9f3d54b057272d8b57fe249223f9

Aliases

arxiv: 1808.07438 · arxiv_version: 1808.07438v2 · doi: 10.48550/arxiv.1808.07438 · pith_short_12: QLZDF5VTEZZ5 · pith_short_16: QLZDF5VTEZZ5LCDV · pith_short_8: QLZDF5VT

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/QLZDF5VTEZZ5LCDVHBGPSXBWNK \
  | 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: 82f232f6b32673d58875384cf95c366ab10e9f3d54b057272d8b57fe249223f9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "096295f24412f2b6e9d49b4b467ad44c467ba90a080132257b6c9eae3dff992c",
    "cross_cats_sorted": [
      "cs.IT",
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2018-08-22T16:59:21Z",
    "title_canon_sha256": "b34af7276846d34182c453acabb2f4a662ee15506b3fd3e49b98936571f7fd82"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1808.07438",
    "kind": "arxiv",
    "version": 2
  }
}