Pith Number

pith:VPLAWXCR

pith:2025:VPLAWXCRQ32KOEZESBBWKC7P7Z

not attested not anchored not stored refs pending

An introduction to real oriented blowups in toric, toroidal and logarithmic geometries

Patrick Popescu-Pampu

arxiv:2507.11982 v1 · 2025-07-16 · 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{VPLAWXCRQ32KOEZESBBWKC7P7Z}

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	2026-07-05T11:38:12.376525Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

abd60b5c5186f4a713249043650beffe6e28e79e17886558cad685efe88311ea

Aliases

arxiv: 2507.11982 · arxiv_version: 2507.11982v1 · doi: 10.48550/arxiv.2507.11982 · pith_short_12: VPLAWXCRQ32K · pith_short_16: VPLAWXCRQ32KOEZE · pith_short_8: VPLAWXCR

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/VPLAWXCRQ32KOEZESBBWKC7P7Z \
  | 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: abd60b5c5186f4a713249043650beffe6e28e79e17886558cad685efe88311ea

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fa8cf4ace310ca25ed734dea29d307b4ddfe930385176a4b1d0c36d939a31284",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2025-07-16T07:25:56Z",
    "title_canon_sha256": "f8df6a0dc03954ff1882c3fd82b31836fa4d33ea9e26093ce1a565f828dce437"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.11982",
    "kind": "arxiv",
    "version": 1
  }
}