Pith Number

pith:Q2S6N7RI

pith:2013:Q2S6N7RIQBM6RP67F4R4JQFGQ2

not attested not anchored not stored refs pending

Logarithmically-small Minors and Topological Minors

Richard Montgomery

arxiv:1309.7886 v2 · 2013-09-30 · 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{Q2S6N7RIQBM6RP67F4R4JQFGQ2}

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	2026-05-18T01:53:09.691580Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

86a5e6fe288059e8bfdf2f23c4c0a68692d0fc65dda6870cfa3802a398f38f4b

Aliases

arxiv: 1309.7886 · arxiv_version: 1309.7886v2 · doi: 10.48550/arxiv.1309.7886 · pith_short_12: Q2S6N7RIQBM6 · pith_short_16: Q2S6N7RIQBM6RP67 · pith_short_8: Q2S6N7RI

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/Q2S6N7RIQBM6RP67F4R4JQFGQ2 \
  | 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: 86a5e6fe288059e8bfdf2f23c4c0a68692d0fc65dda6870cfa3802a398f38f4b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b4d06850f7cd4fd67933f2f75039097145b7dff699367a817ebf99d71b6a83d8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-09-30T15:39:40Z",
    "title_canon_sha256": "7e251de7b3f6bdcc1a4b44524dd3d32419422c59b62a29afb22a949c361e4e3e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.7886",
    "kind": "arxiv",
    "version": 2
  }
}