Pith Number

pith:X7HDXGOB

pith:2024:X7HDXGOB7ISTUZIKARMHWORPSK

not attested not anchored not stored refs pending

Relative Stone-Weierstrass theorem for mappings between varieties

Juliusz Banecki

arxiv:2408.09233 v3 · 2024-08-17 · 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{X7HDXGOB7ISTUZIKARMHWORPSK}

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.

Cited by

1 paper in Pith

Retract rational varieties are uniformly retract rational

Receipt and verification

First computed	2026-07-05T09:54:46.294728Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bfce3b99c1fa253a650a04587b3a2f9287f6b5531d0f89f6740d86ad7bdfd278

Aliases

arxiv: 2408.09233 · arxiv_version: 2408.09233v3 · doi: 10.48550/arxiv.2408.09233 · pith_short_12: X7HDXGOB7IST · pith_short_16: X7HDXGOB7ISTUZIK · pith_short_8: X7HDXGOB

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/X7HDXGOB7ISTUZIKARMHWORPSK \
  | 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: bfce3b99c1fa253a650a04587b3a2f9287f6b5531d0f89f6740d86ad7bdfd278

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c47801b0621eaebff3674b453173b62f26660a5153e32861509abeb13f17e5a4",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2024-08-17T15:46:40Z",
    "title_canon_sha256": "2ff9b2311ff41ce75e14e43c26b2a908e0ab2026df6bfd7dbd344bf4244c02af"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2408.09233",
    "kind": "arxiv",
    "version": 3
  }
}