Pith Number

pith:2TZFJEWB

pith:2021:2TZFJEWBW52D5GBJVCIFLTBA4Q

not attested not anchored not stored refs pending

Dependence over subgroups of free groups

Amnon Rosenmann, Enric Ventura Capell

arxiv:2107.03154 v2 · 2021-07-07 · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2TZFJEWBW52D5GBJVCIFLTBA4Q}

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.

Cited by

1 paper in Pith

Computing $H$-equations with 2-by-2 integral matrices

Receipt and verification

First computed	2026-07-05T06:09:03.412902Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d4f25492c1b7743e9829a89055cc20e43aec8273197291f02f41bbdef461ee87

Aliases

arxiv: 2107.03154 · arxiv_version: 2107.03154v2 · doi: 10.48550/arxiv.2107.03154 · pith_short_12: 2TZFJEWBW52D · pith_short_16: 2TZFJEWBW52D5GBJ · pith_short_8: 2TZFJEWB

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/2TZFJEWBW52D5GBJVCIFLTBA4Q \
  | 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: d4f25492c1b7743e9829a89055cc20e43aec8273197291f02f41bbdef461ee87

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "19da03a836565968a21559396d26cfc3a27ed5a828404028fc53362eb10502f2",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2021-07-07T11:30:24Z",
    "title_canon_sha256": "bb01ab9a99cfc0a960db5d97a91232f9c02d7ad876a7ada977d5c429467ead93"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2107.03154",
    "kind": "arxiv",
    "version": 2
  }
}