Pith Number

pith:DMIFIB7O

pith:2008:DMIFIB7OPBUFLPHMPJUOS3NDYH

not attested not anchored not stored refs pending

Remnant inequalities and doubly-twisted conjugacy in free groups

P. Christopher Staecker

arxiv:0806.4687 v2 · 2008-06-28 · math.AT · 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{DMIFIB7OPBUFLPHMPJUOS3NDYH}

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	2026-05-18T04:23:22.358891Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1b105407ee786855bcec7a68e96da3c1f3a645fe221409d51f10af16e40a4bd8

Aliases

arxiv: 0806.4687 · arxiv_version: 0806.4687v2 · doi: 10.48550/arxiv.0806.4687 · pith_short_12: DMIFIB7OPBUF · pith_short_16: DMIFIB7OPBUFLPHM · pith_short_8: DMIFIB7O

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/DMIFIB7OPBUFLPHMPJUOS3NDYH \
  | 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: 1b105407ee786855bcec7a68e96da3c1f3a645fe221409d51f10af16e40a4bd8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d43127f7c91677ff568975b3f8f1c2965c64a1fb52eba22c8c6ecca7d925fa04",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2008-06-28T14:20:47Z",
    "title_canon_sha256": "b4b1395cc2fcb27e97b806d1e84ae62b3083ebc5421f24bbf515964dee1a8320"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0806.4687",
    "kind": "arxiv",
    "version": 2
  }
}