Pith Number

pith:LK4S2UWD

pith:2012:LK4S2UWDEZS2EDL5IG6AU2EPJA

not attested not anchored not stored refs pending

Stability in the homology of congruence subgroups

Andrew Putman

arxiv:1201.4876 v5 · 2012-01-23 · math.AT · math.GR · math.GT · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LK4S2UWDEZS2EDL5IG6AU2EPJA}

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	2026-05-18T00:50:23.992518Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5ab92d52c32665a20d7d41bc0a688f4834ee1b61a076aeae1cfadff6340e1b0a

Aliases

arxiv: 1201.4876 · arxiv_version: 1201.4876v5 · doi: 10.48550/arxiv.1201.4876 · pith_short_12: LK4S2UWDEZS2 · pith_short_16: LK4S2UWDEZS2EDL5 · pith_short_8: LK4S2UWD

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/LK4S2UWDEZS2EDL5IG6AU2EPJA \
  | 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: 5ab92d52c32665a20d7d41bc0a688f4834ee1b61a076aeae1cfadff6340e1b0a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "35e24b471ff6fdbb3864d94bccbda5bdcd6ca36f215f5ba2df38bd129392f5f0",
    "cross_cats_sorted": [
      "math.GR",
      "math.GT",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2012-01-23T21:28:48Z",
    "title_canon_sha256": "7cb7e6559211b9c3d5c5c872e5f32f67fff3551f5731d9b9983d402af3dcdddf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1201.4876",
    "kind": "arxiv",
    "version": 5
  }
}