Pith Number

pith:ATPEYEC2

pith:2009:ATPEYEC22GGGMJMQPP722JE3G3

not attested not anchored not stored refs pending

A finite separating set for Daigle and Freudenburg's counterexample to Hilbert's Fourteenth Problem

Emilie Dufresne, Martin Kohls

arxiv:0912.0638 v1 · 2009-12-03 · math.AC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ATPEYEC22GGGMJMQPP722JE3G3}

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	2026-05-18T04:31:13.193474Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

04de4c105ad18c6625907bffad249b36d138264c39bb6164cf16ce16c4361851

Aliases

arxiv: 0912.0638 · arxiv_version: 0912.0638v1 · doi: 10.48550/arxiv.0912.0638 · pith_short_12: ATPEYEC22GGG · pith_short_16: ATPEYEC22GGGMJMQ · pith_short_8: ATPEYEC2

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/ATPEYEC22GGGMJMQPP722JE3G3 \
  | 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: 04de4c105ad18c6625907bffad249b36d138264c39bb6164cf16ce16c4361851

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "29f73789cb02fdef7b039f374519b348b26bad94755585f644764d5101e1e5fb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2009-12-03T12:16:11Z",
    "title_canon_sha256": "261e85c3192627811638874fa4c402d6c00f13ea773d8c8f067ce38665eeeffd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0912.0638",
    "kind": "arxiv",
    "version": 1
  }
}