Pith Number

pith:GXO4D2XK

pith:2013:GXO4D2XK6ZBHIYGUVVTEJ3OVPY

not attested not anchored not stored refs pending

Volume gradients and homology in towers of residually-free groups

Dessislava H. Kochloukova, Martin R Bridson

arxiv:1309.1877 v2 · 2013-09-07 · math.GR · math.GT · math.KT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GXO4D2XK6ZBHIYGUVVTEJ3OVPY}

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	2026-05-18T01:17:11.811652Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

35ddc1eaeaf6427460d4ad6644edd57e2266460709d371d405aaa7153399ac91

Aliases

arxiv: 1309.1877 · arxiv_version: 1309.1877v2 · doi: 10.48550/arxiv.1309.1877 · pith_short_12: GXO4D2XK6ZBH · pith_short_16: GXO4D2XK6ZBHIYGU · pith_short_8: GXO4D2XK

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/GXO4D2XK6ZBHIYGUVVTEJ3OVPY \
  | 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: 35ddc1eaeaf6427460d4ad6644edd57e2266460709d371d405aaa7153399ac91

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "55e03300a170997f116aeb7c9df3e02cc1bfc1cb24a0f0d559d5bfba9c657d8a",
    "cross_cats_sorted": [
      "math.GT",
      "math.KT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2013-09-07T15:52:23Z",
    "title_canon_sha256": "770b86ca639151ba6fb7e7164e00275bb97948434110d6a4a564650881636604"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.1877",
    "kind": "arxiv",
    "version": 2
  }
}