Pith Number

pith:LT5NE52K

pith:2019:LT5NE52KWJEYYZHKK2CKTJL7GN

not attested not anchored not stored refs pending

Upper bounds on the graph minor theorem

Martin Krombholz, Michael Rathjen

arxiv:1907.00412 v1 · 2019-06-30 · math.LO · cs.CC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LT5NE52KWJEYYZHKK2CKTJL7GN}

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	2026-05-17T23:41:51.795066Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5cfad2774ab2498c64ea5684a9a57f3372634561dbc60bd66c8ef87e50c5161a

Aliases

arxiv: 1907.00412 · arxiv_version: 1907.00412v1 · doi: 10.48550/arxiv.1907.00412 · pith_short_12: LT5NE52KWJEY · pith_short_16: LT5NE52KWJEYYZHK · pith_short_8: LT5NE52K

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/LT5NE52KWJEYYZHKK2CKTJL7GN \
  | 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: 5cfad2774ab2498c64ea5684a9a57f3372634561dbc60bd66c8ef87e50c5161a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ac7907aa6f7df75eeddea4936d659c0e2248d8829cb87d2b34a52c4c6f0bd166",
    "cross_cats_sorted": [
      "cs.CC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.LO",
    "submitted_at": "2019-06-30T16:41:23Z",
    "title_canon_sha256": "664de87acd12a0c48b992e4e3da668f9347eba8c4d374286993463a306e6849d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1907.00412",
    "kind": "arxiv",
    "version": 1
  }
}