Pith Number

pith:ECIQYJQT

pith:2010:ECIQYJQTS4LJ62Q2LAQTPVVXNL

not attested not anchored not stored refs pending

Line Patterns in Free Groups

Christopher H. Cashen, Natasa Macura

arxiv:1006.2123 v4 · 2010-06-10 · 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{ECIQYJQTS4LJ62Q2LAQTPVVXNL}

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	2026-05-18T02:38:18.474986Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

20910c261397169f6a1a582137d6b76ae4b303ebd82faaa6508978b8098565c5

Aliases

arxiv: 1006.2123 · arxiv_version: 1006.2123v4 · doi: 10.48550/arxiv.1006.2123 · pith_short_12: ECIQYJQTS4LJ · pith_short_16: ECIQYJQTS4LJ62Q2 · pith_short_8: ECIQYJQT

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/ECIQYJQTS4LJ62Q2LAQTPVVXNL \
  | 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: 20910c261397169f6a1a582137d6b76ae4b303ebd82faaa6508978b8098565c5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8a4fce6ddf2a1ced798f2f3d84bef4ba724f7fd4dda8b6714550633c0e365bb2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-06-10T19:33:51Z",
    "title_canon_sha256": "6d1e741eaf8343a03557faaf7920930918a36f3cfa3875cad30d603c3733ce32"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1006.2123",
    "kind": "arxiv",
    "version": 4
  }
}