Pith Number

pith:O4B7FPXC

pith:2025:O4B7FPXCSKMNEZAANNUJWMTSQG

not attested not anchored not stored refs pending

Exotic hypercomplex structures on a torus do not exist

Alberto Pipitone Federico, Misha Verbitsky

arxiv:2506.18179 v1 · 2025-06-22 · math.DG · 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{O4B7FPXCSKMNEZAANNUJWMTSQG}

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	2026-07-05T11:25:30.133444Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7703f2bee29298d264006b689b327281a3770aeb9d668ac4c2eeaae36539a726

Aliases

arxiv: 2506.18179 · arxiv_version: 2506.18179v1 · doi: 10.48550/arxiv.2506.18179 · pith_short_12: O4B7FPXCSKMN · pith_short_16: O4B7FPXCSKMNEZAA · pith_short_8: O4B7FPXC

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/O4B7FPXCSKMNEZAANNUJWMTSQG \
  | 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: 7703f2bee29298d264006b689b327281a3770aeb9d668ac4c2eeaae36539a726

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6b5b55619bf29d1b42c94d435634f9bdab58f55ba80df368e9a1f2b1ff2dd649",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2025-06-22T21:25:59Z",
    "title_canon_sha256": "b4d731d972f29d389308707c5dab7439548ebd381f5d2aa004a3bf71b4a1e22a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.18179",
    "kind": "arxiv",
    "version": 1
  }
}