Pith Number

pith:ANR5FZOA

pith:2010:ANR5FZOAWWLH2GOL7DPQEW3NUR

not attested not anchored not stored refs pending

Cofinitely Hopfian groups, open mappings and knot complements

Daniel Groves, Gaven J. Martin, Jonathan A. Hillman, Martin R. Bridson

arxiv:1012.1785 v1 · 2010-12-08 · 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{ANR5FZOAWWLH2GOL7DPQEW3NUR}

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	2026-05-18T04:33:51.264983Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0363d2e5c0b5967d19cbf8df025b6da46b66e69d03be007273e35ce7855548e5

Aliases

arxiv: 1012.1785 · arxiv_version: 1012.1785v1 · doi: 10.48550/arxiv.1012.1785 · pith_short_12: ANR5FZOAWWLH · pith_short_16: ANR5FZOAWWLH2GOL · pith_short_8: ANR5FZOA

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/ANR5FZOAWWLH2GOL7DPQEW3NUR \
  | 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: 0363d2e5c0b5967d19cbf8df025b6da46b66e69d03be007273e35ce7855548e5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6b4ce6c620303032c8db0e05f5cfffa1ac9c48b3a271833766e5ad912bbfcdfc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-12-08T15:28:32Z",
    "title_canon_sha256": "d14e7e706fa39231200e799c58811446b06c72804c7ff67b3277e53a71ea9d8e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.1785",
    "kind": "arxiv",
    "version": 1
  }
}