Pith Number

pith:KDXMDCOK

pith:2025:KDXMDCOKOD4GMBWS7GD2DPKWME

not attested not anchored not stored refs pending

On probabilistic identities and coset identities in pro-$p$ groups

Matteo Vannacci, Nowras Otmen, Steffen Kionke, Thomas Weigel, Tommaso Toti

arxiv:2507.19086 v2 · 2025-07-25 · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KDXMDCOKOD4GMBWS7GD2DPKWME}

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	2026-05-29T02:05:35.632663Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

50eec189ca70f86606d2f987a1bd56612d625c0ae81a0b96f4c8c798d6017dd4

Aliases

arxiv: 2507.19086 · arxiv_version: 2507.19086v2 · doi: 10.48550/arxiv.2507.19086 · pith_short_12: KDXMDCOKOD4G · pith_short_16: KDXMDCOKOD4GMBWS · pith_short_8: KDXMDCOK

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/KDXMDCOKOD4GMBWS7GD2DPKWME \
  | 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: 50eec189ca70f86606d2f987a1bd56612d625c0ae81a0b96f4c8c798d6017dd4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "993cefafdc1d1d13852baf79911d6b001835a2c1c5e881703340e39762a373a9",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2025-07-25T09:12:30Z",
    "title_canon_sha256": "8302366a8c8da2bd33439ad7e7663fe778d50d3f2f966ca00c63372eaf26c9da"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.19086",
    "kind": "arxiv",
    "version": 2
  }
}