Pith Number

pith:5UPZ45UI

pith:2012:5UPZ45UIQUUBHZGOGOPSPMZGMQ

not attested not anchored not stored refs pending

An analogue of Fekete's lemma for subadditive functions on cancellative amenable semigroups

Fabrice Krieger, Michel Coornaert, Tullio Ceccherini-Silberstein

arxiv:1209.6179 v1 · 2012-09-27 · math.GR · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5UPZ45UIQUUBHZGOGOPSPMZGMQ}

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	2026-05-18T02:17:01.691864Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ed1f9e7688852813e4ce339f27b326642ec4299dddc0bcb8556b2216aa2f6fb1

Aliases

arxiv: 1209.6179 · arxiv_version: 1209.6179v1 · doi: 10.48550/arxiv.1209.6179 · pith_short_12: 5UPZ45UIQUUB · pith_short_16: 5UPZ45UIQUUBHZGO · pith_short_8: 5UPZ45UI

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/5UPZ45UIQUUBHZGOGOPSPMZGMQ \
  | 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: ed1f9e7688852813e4ce339f27b326642ec4299dddc0bcb8556b2216aa2f6fb1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d4d1bbf5ea8e39c243ab34664d6fdcf43941764801ea299138d9419d8a244328",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-09-27T10:11:59Z",
    "title_canon_sha256": "6c255a2f49ff989ba4ccdbcfa6516ac8d4cb39b10210002a2b6e4120b0aad6d3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.6179",
    "kind": "arxiv",
    "version": 1
  }
}