Pith Number

pith:XTDBRNFW

pith:2021:XTDBRNFWWCSV7QRT5QO7SZFLFV

not attested not anchored not stored refs pending

Extremal functions for sparse minors

David R. Wood, Kevin Hendrey, Sergey Norin

arxiv:2107.08658 v3 · 2021-07-19 · 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{XTDBRNFWWCSV7QRT5QO7SZFLFV}

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	2026-07-05T04:42:31.011811Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bcc618b4b6b0a55fc233ec1df964ab2d545bdefbde36f059d60412a3e38edb4c

Aliases

arxiv: 2107.08658 · arxiv_version: 2107.08658v3 · doi: 10.48550/arxiv.2107.08658 · pith_short_12: XTDBRNFWWCSV · pith_short_16: XTDBRNFWWCSV7QRT · pith_short_8: XTDBRNFW

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/XTDBRNFWWCSV7QRT5QO7SZFLFV \
  | 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: bcc618b4b6b0a55fc233ec1df964ab2d545bdefbde36f059d60412a3e38edb4c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b16e08175b765d59d5fd24b80072bfe51f239b340aff802fd5edb782ca589dd8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2021-07-19T07:37:59Z",
    "title_canon_sha256": "04e51c41db4aefe2059b9625843ada0c0a2c7e748867a1fa4fa9b7efb9ac8b87"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2107.08658",
    "kind": "arxiv",
    "version": 3
  }
}