Pith Number

pith:ZOK2NYG7

pith:2026:ZOK2NYG7UOGZAF7O44Q5MEP7S7

not attested not anchored not stored refs pending

Virtual Surjection and the $n$-$(n+1)$-$(n+2)$ Theorem for Profinite Groups

Mark Shusterman, Tal Cohen

arxiv:2606.23600 v1 · 2026-06-22 · 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{ZOK2NYG7UOGZAF7O44Q5MEP7S7}

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	2026-06-23T03:14:31.943123Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cb95a6e0dfa38d9017eee721d611ff97eff6b6d70ea094d4001c8443501f20c0

Aliases

arxiv: 2606.23600 · arxiv_version: 2606.23600v1 · doi: 10.48550/arxiv.2606.23600 · pith_short_12: ZOK2NYG7UOGZ · pith_short_16: ZOK2NYG7UOGZAF7O · pith_short_8: ZOK2NYG7

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/ZOK2NYG7UOGZAF7O44Q5MEP7S7 \
  | 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: cb95a6e0dfa38d9017eee721d611ff97eff6b6d70ea094d4001c8443501f20c0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c92f39a67d2d270d24e0fe005621c4e85233d550d285d524746eaeb12fcd12be",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2026-06-22T17:03:41Z",
    "title_canon_sha256": "a123e879115a4a988b80625dd28960db9b97f238c85761a11d2c09c1d57174db"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.23600",
    "kind": "arxiv",
    "version": 1
  }
}