Pith Number

pith:ZTOJLEVX

pith:2008:ZTOJLEVXIQOAJGZICAMQVMPDBH

not attested not anchored not stored refs pending

Intersection of subgroups in free groups and homotopy groups

Hans-Joachim Baues, Roman Mikhailov

arxiv:0804.1999 v1 · 2008-04-12 · 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{ZTOJLEVXIQOAJGZICAMQVMPDBH}

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	2026-05-18T04:41:36.900641Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ccdc9592b7441c049b2810190ab1e309e1422aa07922a626289d748044dbf6fd

Aliases

arxiv: 0804.1999 · arxiv_version: 0804.1999v1 · doi: 10.48550/arxiv.0804.1999 · pith_short_12: ZTOJLEVXIQOA · pith_short_16: ZTOJLEVXIQOAJGZI · pith_short_8: ZTOJLEVX

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/ZTOJLEVXIQOAJGZICAMQVMPDBH \
  | 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: ccdc9592b7441c049b2810190ab1e309e1422aa07922a626289d748044dbf6fd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d5df0cd725358ba977f4b0a33e6fa9e73c3cfc47dd34f84f23fc7be5c49bedc5",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2008-04-12T07:36:35Z",
    "title_canon_sha256": "c0c5e412bfb506a52c4887f92558a591c892f5bec6b1d49c3073dea3aa8f895c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0804.1999",
    "kind": "arxiv",
    "version": 1
  }
}