Pith Number

pith:TQMA3C4J

pith:2010:TQMA3C4JM2LVOSSRB5YQKZDGAC

not attested not anchored not stored refs pending

Geometric approach to stable homotopy groups of spheres, III. Abelian, cyclic and quaternionic structure for mappings with singularities

Petr M. Akhmet'ev

arxiv:1007.2805 v3 · 2010-07-16 · 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{TQMA3C4JM2LVOSSRB5YQKZDGAC}

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	2026-05-18T04:03:54.716027Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9c180d8b896697574a510f7105646600a241bdfe597a3f456eca18cee029ce87

Aliases

arxiv: 1007.2805 · arxiv_version: 1007.2805v3 · doi: 10.48550/arxiv.1007.2805 · pith_short_12: TQMA3C4JM2LV · pith_short_16: TQMA3C4JM2LVOSSR · pith_short_8: TQMA3C4J

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/TQMA3C4JM2LVOSSRB5YQKZDGAC \
  | 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: 9c180d8b896697574a510f7105646600a241bdfe597a3f456eca18cee029ce87

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5da8faa9cafc7fe499e5381929f5220a42d5194f12811c5dd9cf0fde99abf3de",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2010-07-16T16:20:40Z",
    "title_canon_sha256": "8d75f049931234eee0bcc562bda3752c9a45dbe66a61d37acdbb4a78a51b5a51"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1007.2805",
    "kind": "arxiv",
    "version": 3
  }
}