Pith Number

pith:EPK5XFJC

pith:2008:EPK5XFJCMSLIMRWGL2GVZMOVT4

not attested not anchored not stored refs pending

Bieri-Neumann-Strebel-Renz invariants and homology jumping loci

Alexander I. Suciu, Stefan Papadima

arxiv:0812.2660 v2 · 2008-12-14 · math.GR · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{EPK5XFJCMSLIMRWGL2GVZMOVT4}

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	2026-05-18T04:08:04.223523Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

23d5db952264968646c65e8d5cb1d59f3b3f9711d425be3b8cd6c4e9ab9a1ece

Aliases

arxiv: 0812.2660 · arxiv_version: 0812.2660v2 · doi: 10.48550/arxiv.0812.2660 · pith_short_12: EPK5XFJCMSLI · pith_short_16: EPK5XFJCMSLIMRWG · pith_short_8: EPK5XFJC

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/EPK5XFJCMSLIMRWGL2GVZMOVT4 \
  | 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: 23d5db952264968646c65e8d5cb1d59f3b3f9711d425be3b8cd6c4e9ab9a1ece

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "418d4aa9aab8542e44f052f03c87881844761a6cad345b1f8d13cfdb2b9bca73",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2008-12-14T16:30:19Z",
    "title_canon_sha256": "d0722804083fdf6cd02650c24999a449bb17f1b583b8f738dcf1b79eef6389f4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0812.2660",
    "kind": "arxiv",
    "version": 2
  }
}