Pith Number

pith:HZJQEEC2

pith:2020:HZJQEEC2SQ6KLEZPANHRA5CTVM

not attested not anchored not stored refs pending

Tight gaps in the cycle spectrum of 3-connected planar graphs

On-Hei Solomon Lo, Qing Cui

arxiv:2009.02503 v2 · 2020-09-05 · 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{HZJQEEC2SQ6KLEZPANHRA5CTVM}

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	2026-07-05T01:35:38.132214Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3e5302105a943ca5932f034f107453ab29443986d9fee0fd09ea6b84f01aa313

Aliases

arxiv: 2009.02503 · arxiv_version: 2009.02503v2 · doi: 10.48550/arxiv.2009.02503 · pith_short_12: HZJQEEC2SQ6K · pith_short_16: HZJQEEC2SQ6KLEZP · pith_short_8: HZJQEEC2

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/HZJQEEC2SQ6KLEZPANHRA5CTVM \
  | 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: 3e5302105a943ca5932f034f107453ab29443986d9fee0fd09ea6b84f01aa313

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a65ae57f8930ef909dc593db5526084426d489d9bf2aaf7f92a64ac9d097d306",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2020-09-05T10:05:56Z",
    "title_canon_sha256": "4ba4fb8711988b8e3bdb57bf7f9fc89befd3161c41d54c3df969b72722ec4dbd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2009.02503",
    "kind": "arxiv",
    "version": 2
  }
}