Pith Number

pith:R5KZZOZE

pith:2009:R5KZZOZE32SLGZRFHBYTKQQE75

not attested not anchored not stored refs pending

Presentations of Graph Braid Groups

Daniel Farley, Lucas Sabalka

arxiv:0907.2730 v1 · 2009-07-16 · 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{R5KZZOZE32SLGZRFHBYTKQQE75}

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	2026-05-18T04:11:08.880382Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8f559cbb24dea4b366253871354204ff4f5b7c4903f0addca6a1d3690facc3c4

Aliases

arxiv: 0907.2730 · arxiv_version: 0907.2730v1 · doi: 10.48550/arxiv.0907.2730 · pith_short_12: R5KZZOZE32SL · pith_short_16: R5KZZOZE32SLGZRF · pith_short_8: R5KZZOZE

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/R5KZZOZE32SLGZRFHBYTKQQE75 \
  | 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: 8f559cbb24dea4b366253871354204ff4f5b7c4903f0addca6a1d3690facc3c4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f81305adfc6b251f722275a609ba370f29fd1821b0336d4dbfbd26964a8a93c4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2009-07-16T02:04:22Z",
    "title_canon_sha256": "84cb26af994289546158e746193f24d88f781518fb4f282b29349a51002a0b4e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0907.2730",
    "kind": "arxiv",
    "version": 1
  }
}