Pith Number

pith:D6GVYLMB

pith:2011:D6GVYLMB7NWEZ3BRR3QFQEQOLE

not attested not anchored not stored refs pending

Homotopy invariance of non-stable K_1-functors

Anastasia Stavrova

arxiv:1111.4664 v5 · 2011-11-20 · math.AG · math.GR · math.KT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{D6GVYLMB7NWEZ3BRR3QFQEQOLE}

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	2026-05-18T03:33:50.195465Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1f8d5c2d81fb6c4cec318ee058120e591db27299e7fe1aebc053ca73f74069b8

Aliases

arxiv: 1111.4664 · arxiv_version: 1111.4664v5 · doi: 10.48550/arxiv.1111.4664 · pith_short_12: D6GVYLMB7NWE · pith_short_16: D6GVYLMB7NWEZ3BR · pith_short_8: D6GVYLMB

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/D6GVYLMB7NWEZ3BRR3QFQEQOLE \
  | 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: 1f8d5c2d81fb6c4cec318ee058120e591db27299e7fe1aebc053ca73f74069b8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6fa5abfcaac3c5b21510ad3569ace08dfa24086e1baa7947fd91b4f201e8d10f",
    "cross_cats_sorted": [
      "math.GR",
      "math.KT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2011-11-20T19:01:25Z",
    "title_canon_sha256": "ebb7ee045748f6d903c496ca066eabbc8bf31e3030438d88de6aa0212c003d20"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.4664",
    "kind": "arxiv",
    "version": 5
  }
}