Pith Number

pith:3XT4LDLZ

pith:2021:3XT4LDLZHKWTWUTOQ4C4HGS7AQ

not attested not anchored not stored refs pending

Linearity and indiscreteness of amalgamated products of hyperbolic groups

Konstantinos Tsouvalas, Nicolas Tholozan

arxiv:2112.05574 v2 · 2021-12-10 · 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{3XT4LDLZHKWTWUTOQ4C4HGS7AQ}

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	2026-07-05T04:34:27.271074Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dde7c58d793aad3b526e8705c39a5f043d35d9324985b70086caddd9c02d20eb

Aliases

arxiv: 2112.05574 · arxiv_version: 2112.05574v2 · doi: 10.48550/arxiv.2112.05574 · pith_short_12: 3XT4LDLZHKWT · pith_short_16: 3XT4LDLZHKWTWUTO · pith_short_8: 3XT4LDLZ

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/3XT4LDLZHKWTWUTOQ4C4HGS7AQ \
  | 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: dde7c58d793aad3b526e8705c39a5f043d35d9324985b70086caddd9c02d20eb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a4067fcbef4939a040e01143305fd03dfd12ea9009080dd128058a9e51cbc2fd",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2021-12-10T14:42:44Z",
    "title_canon_sha256": "38f4a59fce81d19802bfd8b6679c56ed9544e08c13a97ac51f02236c221179b3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2112.05574",
    "kind": "arxiv",
    "version": 2
  }
}