Pith Number

pith:7XFM53IS

pith:2016:7XFM53ISBOAZ3QYY6WRAKPA6TI

not attested not anchored not stored refs pending

Wrong way maps in uniformly finite homology and homology of groups

Alexander Engel

arxiv:1602.03374 v4 · 2016-02-10 · math.GT · math.AT · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7XFM53ISBOAZ3QYY6WRAKPA6TI}

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	2026-05-17T23:49:44.529708Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fdcaceed120b819dc318f5a2053c1e9a019621f2b23dbfec744e1fdecfcf7125

Aliases

arxiv: 1602.03374 · arxiv_version: 1602.03374v4 · doi: 10.48550/arxiv.1602.03374 · pith_short_12: 7XFM53ISBOAZ · pith_short_16: 7XFM53ISBOAZ3QYY · pith_short_8: 7XFM53IS

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/7XFM53ISBOAZ3QYY6WRAKPA6TI \
  | 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: fdcaceed120b819dc318f5a2053c1e9a019621f2b23dbfec744e1fdecfcf7125

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "84413b79cbb4238d7b8105f7335c4a0d6f7050714affc7d6e38cef595aa03cd7",
    "cross_cats_sorted": [
      "math.AT",
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2016-02-10T14:06:46Z",
    "title_canon_sha256": "58e1357b95ff74d65475a3b71273cb96d03d1c914b2219249052307cbbaffa56"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1602.03374",
    "kind": "arxiv",
    "version": 4
  }
}