Pith Number

pith:LXXTPRRP

pith:2007:LXXTPRRPGAP6AF7BNMLFLGUU43

not attested not anchored not stored refs pending

On fundamental groups related to the Hirzebruch surface F_1

Michael Friedman, Mina Teicher

arxiv:0706.1680 v1 · 2007-06-12 · 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{LXXTPRRPGAP6AF7BNMLFLGUU43}

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	2026-05-18T02:16:30.192637Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5def37c62f301fe017e16b16559a94e6d9c8e46eb971dcfc0565dc4dd0888e3f

Aliases

arxiv: 0706.1680 · arxiv_version: 0706.1680v1 · doi: 10.48550/arxiv.0706.1680 · pith_short_12: LXXTPRRPGAP6 · pith_short_16: LXXTPRRPGAP6AF7B · pith_short_8: LXXTPRRP

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/LXXTPRRPGAP6AF7BNMLFLGUU43 \
  | 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: 5def37c62f301fe017e16b16559a94e6d9c8e46eb971dcfc0565dc4dd0888e3f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7231cb76536dea69484487ab2f173bcd65b4e123c78f7d1ac8911a090312ecb2",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.AG",
    "submitted_at": "2007-06-12T13:06:53Z",
    "title_canon_sha256": "5e209b7fcde86d786ecfa229363350649055ad4d0e415929e754b93046bb2c85"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0706.1680",
    "kind": "arxiv",
    "version": 1
  }
}