Pith Number

pith:YLMIRG4F

pith:2012:YLMIRG4FKCBWZLODZ7XB6Q74CL

not attested not anchored not stored refs pending

On the growth of Betti numbers in $p$-adic analytic towers

Nicolas Bergeron, Peter Linnell, Roman Sauer, Wolfgang L\"uck

arxiv:1204.3298 v3 · 2012-04-15 · math.GT · math.KT · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YLMIRG4FKCBWZLODZ7XB6Q74CL}

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	2026-05-18T03:30:28.133184Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c2d8889b8550836cadc3cfee1f43fc12fe03427aa262b9978d71d9a093f660c9

Aliases

arxiv: 1204.3298 · arxiv_version: 1204.3298v3 · doi: 10.48550/arxiv.1204.3298 · pith_short_12: YLMIRG4FKCBW · pith_short_16: YLMIRG4FKCBWZLOD · pith_short_8: YLMIRG4F

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/YLMIRG4FKCBWZLODZ7XB6Q74CL \
  | 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: c2d8889b8550836cadc3cfee1f43fc12fe03427aa262b9978d71d9a093f660c9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ce7b6be3183417f1c4c1b6daba0c73222911e169e8f6479818c78575ccb66017",
    "cross_cats_sorted": [
      "math.KT",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2012-04-15T18:02:32Z",
    "title_canon_sha256": "3b13669fcd31d6ab8df6bdcb1b6e6ffc3eb1f65854d69b0adb2e669d7fa18345"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.3298",
    "kind": "arxiv",
    "version": 3
  }
}