Pith Number

pith:6Q5MQYGM

pith:2016:6Q5MQYGMJ7I5DSE2V77VARVWD2

not attested not anchored not stored refs pending

The Cohomology of canonical quotients of free groups and Lyndon words

Ido Efrat

arxiv:1604.07566 v2 · 2016-04-26 · math.NT · 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{6Q5MQYGMJ7I5DSE2V77VARVWD2}

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	2026-05-18T00:44:52.507199Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f43ac860cc4fd1d1c89aafff5046b61ea2aa36a156ebcaceb03a5c23845343e5

Aliases

arxiv: 1604.07566 · arxiv_version: 1604.07566v2 · doi: 10.48550/arxiv.1604.07566 · pith_short_12: 6Q5MQYGMJ7I5 · pith_short_16: 6Q5MQYGMJ7I5DSE2 · pith_short_8: 6Q5MQYGM

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/6Q5MQYGMJ7I5DSE2V77VARVWD2 \
  | 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: f43ac860cc4fd1d1c89aafff5046b61ea2aa36a156ebcaceb03a5c23845343e5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5fba319c551ee314f81ca5d3ad0bb9b5a1e6cf390f02d1808c8ae728b0dc5514",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-04-26T08:35:47Z",
    "title_canon_sha256": "db0fae7f671b1ebfe5235f9e138d64585f95f54614708ed33aaee5c714867753"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1604.07566",
    "kind": "arxiv",
    "version": 2
  }
}