Pith Number

pith:JRSNGO3Q

pith:2014:JRSNGO3QLHD5QTEJC7LXKW2GL4

not attested not anchored not stored refs pending

Unbounded asymmetry of stretch factors

Christopher J Leininger, Ilya Kapovich, Spencer Dowdall

arxiv:1405.0771 v1 · 2014-05-05 · 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{JRSNGO3QLHD5QTEJC7LXKW2GL4}

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	2026-05-18T01:35:40.363813Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4c64d33b7059c7d84c8917d7755b465f0ffc6344d068a20ef6b43040b0274324

Aliases

arxiv: 1405.0771 · arxiv_version: 1405.0771v1 · doi: 10.48550/arxiv.1405.0771 · pith_short_12: JRSNGO3QLHD5 · pith_short_16: JRSNGO3QLHD5QTEJ · pith_short_8: JRSNGO3Q

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/JRSNGO3QLHD5QTEJC7LXKW2GL4 \
  | 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: 4c64d33b7059c7d84c8917d7755b465f0ffc6344d068a20ef6b43040b0274324

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4e4d490ea6782e1c5aebe8fdc0f8531f83f7a73a4fa55915899b2a0e7151f334",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2014-05-05T03:12:00Z",
    "title_canon_sha256": "e01629332822d68e56703080d9accdeb11b7cea2bd76803e318f78cf3464f013"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1405.0771",
    "kind": "arxiv",
    "version": 1
  }
}