Pith Number

pith:MTNH3JOS

pith:2012:MTNH3JOSGRH6VLSOHRG7GU2UMQ

not attested not anchored not stored refs pending

Borel stability for congruence subgroups

David Bruce Cohen

arxiv:1207.6725 v3 · 2012-07-28 · math.AT · math.KT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MTNH3JOSGRH6VLSOHRG7GU2UMQ}

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	2026-05-18T00:45:08.909703Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

64da7da5d2344feaae4e3c4df35354641cea42040cb8fbd3ab3715c42ef7e9f6

Aliases

arxiv: 1207.6725 · arxiv_version: 1207.6725v3 · doi: 10.48550/arxiv.1207.6725 · pith_short_12: MTNH3JOSGRH6 · pith_short_16: MTNH3JOSGRH6VLSO · pith_short_8: MTNH3JOS

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/MTNH3JOSGRH6VLSOHRG7GU2UMQ \
  | 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: 64da7da5d2344feaae4e3c4df35354641cea42040cb8fbd3ab3715c42ef7e9f6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "29ea41dd6d39b7369b3dd3d49eb83c9ecad5b5a7f88918d79c6e14fc683c6719",
    "cross_cats_sorted": [
      "math.KT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2012-07-28T20:19:56Z",
    "title_canon_sha256": "1994360dc289007f7d85fe7af11c897b8612bc9f25a8bc3a9186f2ac826095a5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.6725",
    "kind": "arxiv",
    "version": 3
  }
}