Pith Number

pith:M4DMSZFL

pith:2026:M4DMSZFLFAOF4Q4PSPEYFITMFF

not attested not anchored not stored refs pending

Finite Group Reduction of the DR/DZ Hierarchies

Si-Qi Liu, Tianwen Zhong, Youjin Zhang

arxiv:2607.16607 v1 · 2026-07-18 · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{M4DMSZFLFAOF4Q4PSPEYFITMFF}

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	2026-07-21T00:20:27.979942Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6706c964ab281c5e438f93c982a26c2976fb3b12b2dfd347c71b409296a26a83

Aliases

arxiv: 2607.16607 · arxiv_version: 2607.16607v1 · doi: 10.48550/arxiv.2607.16607 · pith_short_12: M4DMSZFLFAOF · pith_short_16: M4DMSZFLFAOF4Q4P · pith_short_8: M4DMSZFL

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/M4DMSZFLFAOF4Q4PSPEYFITMFF \
  | 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: 6706c964ab281c5e438f93c982a26c2976fb3b12b2dfd347c71b409296a26a83

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dfa2bb4f2cfd785eb303c6f2a1757498e08b4c18493590956710e6e75ef58ac0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2026-07-18T03:05:34Z",
    "title_canon_sha256": "0fd13a94114a27ea9c16841e2b05c2d6b2070d42dfe29c4ba8495e54bb5fe772"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.16607",
    "kind": "arxiv",
    "version": 1
  }
}