Pith Number

pith:HQX2FOMO

pith:2025:HQX2FOMOLRHOM3SMXULHKJHMJP

not attested not anchored not stored refs pending

Minimal tori in $\mathbb{R}^4$

Marc Soret, Marina Ville

arxiv:2507.12914 v2 · 2025-07-17 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HQX2FOMOLRHOM3SMXULHKJHMJP}

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	2026-07-05T12:01:24.897677Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3c2fa2b98e5c4ee66e4cbd167524ec4be3b07ef0fbba70073a42f0574349b3a7

Aliases

arxiv: 2507.12914 · arxiv_version: 2507.12914v2 · doi: 10.48550/arxiv.2507.12914 · pith_short_12: HQX2FOMOLRHO · pith_short_16: HQX2FOMOLRHOM3SM · pith_short_8: HQX2FOMO

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/HQX2FOMOLRHOM3SMXULHKJHMJP \
  | 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: 3c2fa2b98e5c4ee66e4cbd167524ec4be3b07ef0fbba70073a42f0574349b3a7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "10de26755f6f3e95e17137de7e4546e002ff43e72afafcf3bcbfa5da74af1aa3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2025-07-17T09:00:22Z",
    "title_canon_sha256": "255ecfd6caf7ad339c3791670bc44793fc750fa0f557ad8eb885eb804c6417f8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.12914",
    "kind": "arxiv",
    "version": 2
  }
}