Pith Number

pith:XXMBPGD2

pith:2016:XXMBPGD23L76YKLSVO7IELJZUF

not attested not anchored not stored refs pending

On the local density problem for graphs of given odd-girth

Christian Reiher, Guilherme Oliveira Mota, Mathias Schacht, Wiebke Bedenknecht

arxiv:1609.05712 v2 · 2016-09-19 · 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{XXMBPGD23L76YKLSVO7IELJZUF}

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	2026-05-17T23:52:19.152739Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bdd817987adaffec2972abbe822d39a15aaa783cc5523adc960561aaffcdd631

Aliases

arxiv: 1609.05712 · arxiv_version: 1609.05712v2 · doi: 10.48550/arxiv.1609.05712 · pith_short_12: XXMBPGD23L76 · pith_short_16: XXMBPGD23L76YKLS · pith_short_8: XXMBPGD2

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/XXMBPGD23L76YKLSVO7IELJZUF \
  | 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: bdd817987adaffec2972abbe822d39a15aaa783cc5523adc960561aaffcdd631

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "88d5c97ebb3b6d0f52813a2e241f8ebd12c626e6b3d233298def72bfbfd93d44",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-09-19T13:25:33Z",
    "title_canon_sha256": "d9843dbadcf8d746ad4a5f87171c3b2c52732ebb522ff5e6e8ce35260b835c45"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.05712",
    "kind": "arxiv",
    "version": 2
  }
}