Pith Number

pith:67QV74TU

pith:2012:67QV74TUMXOUHGLRKRV4J4LZX3

not attested not anchored not stored refs pending

The fundamental group of a locally finite graph with ends: a hyperfinite approach

Alessandro Sisto, Isaac Goldbring

arxiv:1203.4609 v2 · 2012-03-20 · math.GT · math.CO · math.LO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{67QV74TUMXOUHGLRKRV4J4LZX3}

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	2026-05-18T03:59:02.757432Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f7e15ff27465dd439971546bc4f179bec1c90cc4ea17f9fc25aa3db75e673174

Aliases

arxiv: 1203.4609 · arxiv_version: 1203.4609v2 · doi: 10.48550/arxiv.1203.4609 · pith_short_12: 67QV74TUMXOU · pith_short_16: 67QV74TUMXOUHGLR · pith_short_8: 67QV74TU

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/67QV74TUMXOUHGLRKRV4J4LZX3 \
  | 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: f7e15ff27465dd439971546bc4f179bec1c90cc4ea17f9fc25aa3db75e673174

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2af96f5696748746013ca8d4b354f4410c8d919ac06a9c902459bc76e7eba69a",
    "cross_cats_sorted": [
      "math.CO",
      "math.LO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2012-03-20T22:17:42Z",
    "title_canon_sha256": "94a560c1c6a04a50bdeeccd26a9b9b9798240ac2b62c7adfdf79757550a75de9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.4609",
    "kind": "arxiv",
    "version": 2
  }
}