Pith Number

pith:OM4TZEF7

pith:2008:OM4TZEF7NMYCY6MY67N2OPZCQW

not attested not anchored not stored refs pending

On the symmetry of b-functions of linear free divisors

Mathias Schulze, Michel Granger

arxiv:0807.0560 v2 · 2008-07-03 · math.AG · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OM4TZEF7NMYCY6MY67N2OPZCQW}

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	2026-05-18T04:31:21.186115Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

73393c90bf6b302c7998f7dba73f22859e69cf6ea6fae77015b195c70fcbf683

Aliases

arxiv: 0807.0560 · arxiv_version: 0807.0560v2 · doi: 10.48550/arxiv.0807.0560 · pith_short_12: OM4TZEF7NMYC · pith_short_16: OM4TZEF7NMYCY6MY · pith_short_8: OM4TZEF7

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/OM4TZEF7NMYCY6MY67N2OPZCQW \
  | 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: 73393c90bf6b302c7998f7dba73f22859e69cf6ea6fae77015b195c70fcbf683

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "38e39cd8ec34d24c8cbc9de8dd54fe9fbef0e896a671e005257bcbd368c4d115",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2008-07-03T13:32:02Z",
    "title_canon_sha256": "9c6e01f104b3006ae3fb1dd1566fe447a76331b806c4c1e2fb1ed23e95c37ed6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0807.0560",
    "kind": "arxiv",
    "version": 2
  }
}