Pith Number

pith:E3TGE3LX

pith:2026:E3TGE3LXMVBG4XD6GIL4W7FJZT

not attested not anchored not stored refs pending

Brownian motion: the hyperbolic number setting

Daniel Alpay, Ilwoo Cho, Liora Mayats-Alpay

arxiv:2605.30616 v1 · 2026-05-28 · math.PR · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{E3TGE3LXMVBG4XD6GIL4W7FJZT}

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	2026-06-01T01:03:04.137883Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

26e6626d7765426e5c7e3217cb7ca9ccd199c778469baaeeaba3d0c6fa0a002a

Aliases

arxiv: 2605.30616 · arxiv_version: 2605.30616v1 · doi: 10.48550/arxiv.2605.30616 · pith_short_12: E3TGE3LXMVBG · pith_short_16: E3TGE3LXMVBG4XD6 · pith_short_8: E3TGE3LX

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/E3TGE3LXMVBG4XD6GIL4W7FJZT \
  | 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: 26e6626d7765426e5c7e3217cb7ca9ccd199c778469baaeeaba3d0c6fa0a002a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ca0bf510fadcf29018c0bfc452733cf2283aa664cd2b3037fd06f2a9fc2e584f",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-05-28T22:08:29Z",
    "title_canon_sha256": "eea1b9fd5ca475e83d19100955bee3fdf571e7a4a045da4414659392cb57b3b5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.30616",
    "kind": "arxiv",
    "version": 1
  }
}