Pith Number

pith:MHSFW3FP

pith:2018:MHSFW3FPDMXFCGWD5K2V6VGKSG

not attested not anchored not stored refs pending

Two comments on balls in vertex transitive graphs

Gady Kozma, Itai Benjamini

arxiv:1803.03805 v2 · 2018-03-10 · math.CO · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MHSFW3FPDMXFCGWD5K2V6VGKSG}

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	2026-05-18T00:21:19.286452Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

61e45b6caf1b2e511ac3eab55f54ca91b043c547eba18da9d33382c38a8dc8f1

Aliases

arxiv: 1803.03805 · arxiv_version: 1803.03805v2 · doi: 10.48550/arxiv.1803.03805 · pith_short_12: MHSFW3FPDMXF · pith_short_16: MHSFW3FPDMXFCGWD · pith_short_8: MHSFW3FP

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/MHSFW3FPDMXFCGWD5K2V6VGKSG \
  | 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: 61e45b6caf1b2e511ac3eab55f54ca91b043c547eba18da9d33382c38a8dc8f1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e70c374ec84239fb00a8704f808d378db8f92d95fd162d49903a7fe01291699d",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2018-03-10T13:39:03Z",
    "title_canon_sha256": "5e72df82d38a30083c8ecd1f6021cd22554dec2cea06fd7989e2f0f70fe1a906"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1803.03805",
    "kind": "arxiv",
    "version": 2
  }
}