Pith Number

pith:MXLH2XX2

pith:2011:MXLH2XX2HWH75IGPDA2ZUGKYCQ

not attested not anchored not stored refs pending

Left-orderings on free products of groups

Crist\'obal Rivas

arxiv:1106.2094 v1 · 2011-06-10 · 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{MXLH2XX2HWH75IGPDA2ZUGKYCQ}

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	2026-05-18T04:20:13.677489Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

65d67d5efa3d8ffea0cf18359a19581407b97212423616b91c9152a114789b25

Aliases

arxiv: 1106.2094 · arxiv_version: 1106.2094v1 · doi: 10.48550/arxiv.1106.2094 · pith_short_12: MXLH2XX2HWH7 · pith_short_16: MXLH2XX2HWH75IGP · pith_short_8: MXLH2XX2

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/MXLH2XX2HWH75IGPDA2ZUGKYCQ \
  | 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: 65d67d5efa3d8ffea0cf18359a19581407b97212423616b91c9152a114789b25

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2dc1dda8b06d5aaa0471bc894fb6cae68a6fae5fd809afd45360939763788e62",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2011-06-10T15:11:57Z",
    "title_canon_sha256": "d3231393404f430002d4cf66c10504887b10bec02f7012fd1bfd49ca3a6ed028"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.2094",
    "kind": "arxiv",
    "version": 1
  }
}