Pith Number

pith:AFXEM6C6

pith:2015:AFXEM6C6D3LZHJY62EIUQTBHGP

not attested not anchored not stored refs pending

High density piecewise syndeticity of product sets in amenable groups

Isaac Goldbring, Karl Mahlburg, Martino Lupini, Mauro Di Nasso, Renling Jin, Steven Leth

arxiv:1505.04701 v2 · 2015-05-18 · math.CO · math.GR · math.LO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AFXEM6C6D3LZHJY62EIUQTBHGP}

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	2026-05-18T01:35:39.741037Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

016e46785e1ed793a71ed111484c2733dd17142dddaec72a79f705b364220a09

Aliases

arxiv: 1505.04701 · arxiv_version: 1505.04701v2 · doi: 10.48550/arxiv.1505.04701 · pith_short_12: AFXEM6C6D3LZ · pith_short_16: AFXEM6C6D3LZHJY6 · pith_short_8: AFXEM6C6

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/AFXEM6C6D3LZHJY62EIUQTBHGP \
  | 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: 016e46785e1ed793a71ed111484c2733dd17142dddaec72a79f705b364220a09

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "195c2739ad164dd50b3ed39ab12cecd72f343cb07e8290f6fe74e38252e9d681",
    "cross_cats_sorted": [
      "math.GR",
      "math.LO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-05-18T16:08:46Z",
    "title_canon_sha256": "458f139eb469d991056c84f9a367238395f6fadaa7695b02ee961a8f8548fed4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.04701",
    "kind": "arxiv",
    "version": 2
  }
}