Pith Number

pith:DS7UAWTO

pith:2024:DS7UAWTOPNQELDPIC3GYCYMERX

not attested not anchored not stored refs pending

Geodesic Trees and Exceptional Directions in FPP on Hyperbolic Groups

Mahan Mj, Riddhipratim Basu

arxiv:2412.03067 v3 · 2024-12-04 · math.PR · math.GR · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DS7UAWTOPNQELDPIC3GYCYMERX}

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	2026-05-17T23:39:18.278955Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1cbf405a6e7b60458de816cd8161848ddbdb5b3b2870ddef3dffb87fdf4e3886

Aliases

arxiv: 2412.03067 · arxiv_version: 2412.03067v3 · doi: 10.48550/arxiv.2412.03067 · pith_short_12: DS7UAWTOPNQE · pith_short_16: DS7UAWTOPNQELDPI · pith_short_8: DS7UAWTO

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/DS7UAWTOPNQELDPIC3GYCYMERX \
  | 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: 1cbf405a6e7b60458de816cd8161848ddbdb5b3b2870ddef3dffb87fdf4e3886

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8adebddf32a754ebcae999f2af715cc647c9e958a688f857bd4d87fc6e21302b",
    "cross_cats_sorted": [
      "math.GR",
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2024-12-04T06:37:47Z",
    "title_canon_sha256": "64b79ba828067890e50590f682ec60f8497bc8cf213d3cdb1b2e2cd8fc872ec5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.03067",
    "kind": "arxiv",
    "version": 3
  }
}