Pith Number

pith:Y53DWALH

pith:2024:Y53DWALHYOWC6FWANO7MC72SBN

not attested not anchored not stored refs pending

Density of growth-rates of subgroups of a free group and the non-backtracking spectrum of the configuration model

Daniel T. Wise, Gal Yehuda, Michail Louvaris

arxiv:2404.07321 v1 · 2024-04-10 · math.GR · math.PR

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

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\usepackage{pith}
\pithnumber{Y53DWALHYOWC6FWANO7MC72SBN}

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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

On the growth spectrum of hyperbolic groups

Receipt and verification

First computed	2026-07-05T08:06:50.866005Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c7763b0167c3ac2f16c06bbec17f520b7b1200fe918839510867523d455a0c20

Aliases

arxiv: 2404.07321 · arxiv_version: 2404.07321v1 · doi: 10.48550/arxiv.2404.07321 · pith_short_12: Y53DWALHYOWC · pith_short_16: Y53DWALHYOWC6FWA · pith_short_8: Y53DWALH

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/Y53DWALHYOWC6FWANO7MC72SBN \
  | 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: c7763b0167c3ac2f16c06bbec17f520b7b1200fe918839510867523d455a0c20

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fa750ba7f951e91d7a9824b670a5790be201730ec494550cef4e1fe51773d658",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2024-04-10T19:49:25Z",
    "title_canon_sha256": "7ef359a36d33b29750bbf5f3969495052217f0a025cc4fa1ad27f43eda91de38"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2404.07321",
    "kind": "arxiv",
    "version": 1
  }
}