Pith Number

pith:YIRMRVCP

pith:2005:YIRMRVCPSBPJBX72BN5N2UURAQ

not attested not anchored not stored refs pending

New lower bounds on subgroup growth and homology growth

Marc Lackenby

arxiv:math/0512261 v3 · 2005-12-13 · math.GR · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YIRMRVCPSBPJBX72BN5N2UURAQ}

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	2026-05-18T02:57:50.997443Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c222c8d44f905e90dffa0b7add5291042e0398eada3e47c1583ddb25998c6647

Aliases

arxiv: math/0512261 · arxiv_version: math/0512261v3 · doi: 10.48550/arxiv.math/0512261 · pith_short_12: YIRMRVCPSBPJ · pith_short_16: YIRMRVCPSBPJBX72 · pith_short_8: YIRMRVCP

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/YIRMRVCPSBPJBX72BN5N2UURAQ \
  | 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: c222c8d44f905e90dffa0b7add5291042e0398eada3e47c1583ddb25998c6647

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dc5b35baa5ff0694aa47d32acd7e6b2bc472265faeb67d8972582d67cdf63d47",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "",
    "primary_cat": "math.GR",
    "submitted_at": "2005-12-13T11:04:39Z",
    "title_canon_sha256": "0b9ad77750fbac77970eaa1bf1c98f1130a8490ccc8f826e2996b995fd61b022"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0512261",
    "kind": "arxiv",
    "version": 3
  }
}