Pith Number

pith:USJ7R2HB

pith:2025:USJ7R2HB6A6I4RXW2JI2QPR5MK

not attested not anchored not stored refs pending

On injectivity of Cohen-Wu homomorphism

Vasily Ionin

arxiv:2507.09636 v1 · 2025-07-13 · 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{USJ7R2HB6A6I4RXW2JI2QPR5MK}

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	2026-07-05T11:36:37.184514Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a493f8e8e1f03c8e46f6d251a83e3d62bc99a5b7c68eb51b92a1321853eed86d

Aliases

arxiv: 2507.09636 · arxiv_version: 2507.09636v1 · doi: 10.48550/arxiv.2507.09636 · pith_short_12: USJ7R2HB6A6I · pith_short_16: USJ7R2HB6A6I4RXW · pith_short_8: USJ7R2HB

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/USJ7R2HB6A6I4RXW2JI2QPR5MK \
  | 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: a493f8e8e1f03c8e46f6d251a83e3d62bc99a5b7c68eb51b92a1321853eed86d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3ad9ed6a2208ca00a389f825b3605dcb2f70d0c4a819dc4af60c0ca32c0a9baf",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2025-07-13T14:04:15Z",
    "title_canon_sha256": "f0b444ab122e9a7291ab12b35cb85b471d952161155aae55ecad14e5df7d9ea0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.09636",
    "kind": "arxiv",
    "version": 1
  }
}