Pith Number

pith:X3A3GWLD

pith:2016:X3A3GWLD7Z7HU5L4TLY7ISDPYK

not attested not anchored not stored refs pending

Linear programming and the intersection of free subgroups in free products of groups

Sergei V. Ivanov

arxiv:1607.03052 v2 · 2016-07-11 · math.GR · math.OC

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{X3A3GWLD7Z7HU5L4TLY7ISDPYK}

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	2026-05-18T00:27:02.967809Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bec1b35963fe7e7a757c9af1f4486fc2a7edf569896c71f4673afa76e3bc6c83

Aliases

arxiv: 1607.03052 · arxiv_version: 1607.03052v2 · doi: 10.48550/arxiv.1607.03052 · pith_short_12: X3A3GWLD7Z7H · pith_short_16: X3A3GWLD7Z7HU5L4 · pith_short_8: X3A3GWLD

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/X3A3GWLD7Z7HU5L4TLY7ISDPYK \
  | 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: bec1b35963fe7e7a757c9af1f4486fc2a7edf569896c71f4673afa76e3bc6c83

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a78777266d14ddb1e6859342f5630bd211cad00ab774d10da1399f473859c523",
    "cross_cats_sorted": [
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2016-07-11T17:33:57Z",
    "title_canon_sha256": "50c117902be5cc0217ee9bc257e63033af8ca5b472e7100fbd229f50aac5407f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1607.03052",
    "kind": "arxiv",
    "version": 2
  }
}