Pith Number

pith:T2O6EGAD

pith:2021:T2O6EGADBPH6YVDMJVBQER3S7B

not attested not anchored not stored refs pending

On homology torsion growth

Damien Gaboriau, Miklos Abert, Mikolaj Fraczyk, Nicolas Bergeron

arxiv:2106.13051 v3 · 2021-06-24 · math.GT · math.AT · math.GR · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{T2O6EGADBPH6YVDMJVBQER3S7B}

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

Applications of Almost Stationarity I: Quantitative Growth of Injectivity Radius and St\"{u}ck-Zimmer Theorem

Receipt and verification

First computed	2026-07-05T05:25:26.708431Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9e9de218030bcfec546c4d43024772f873373a189d29760d379ea86807c77799

Aliases

arxiv: 2106.13051 · arxiv_version: 2106.13051v3 · doi: 10.48550/arxiv.2106.13051 · pith_short_12: T2O6EGADBPH6 · pith_short_16: T2O6EGADBPH6YVDM · pith_short_8: T2O6EGAD

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/T2O6EGADBPH6YVDMJVBQER3S7B \
  | 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: 9e9de218030bcfec546c4d43024772f873373a189d29760d379ea86807c77799

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fb4450de25f9b478c68c05e22c8b33da59e3fe86730318285e3f68fa78ea4c6c",
    "cross_cats_sorted": [
      "math.AT",
      "math.GR",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2021-06-24T14:22:57Z",
    "title_canon_sha256": "0aaa92ef12b8fe8b2b16e2858d026835265e1a4fae4187a983f1145f66ae90b0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2106.13051",
    "kind": "arxiv",
    "version": 3
  }
}