Pith Number

pith:ZR6LMYF5

pith:2012:ZR6LMYF5DVWTYLDIAGPO4GZ7DW

not attested not anchored not stored refs pending

Deloopings of the spaces of long embeddings

Keiichi Sakai

arxiv:1209.5043 v2 · 2012-09-23 · math.GT · 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{ZR6LMYF5DVWTYLDIAGPO4GZ7DW}

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	2026-05-18T02:44:32.551855Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cc7cb660bd1d6d3c2c68019eee1b3f1da0891bea55ade5f69d9803d33480c3a2

Aliases

arxiv: 1209.5043 · arxiv_version: 1209.5043v2 · doi: 10.48550/arxiv.1209.5043 · pith_short_12: ZR6LMYF5DVWT · pith_short_16: ZR6LMYF5DVWTYLDI · pith_short_8: ZR6LMYF5

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/ZR6LMYF5DVWTYLDIAGPO4GZ7DW \
  | 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: cc7cb660bd1d6d3c2c68019eee1b3f1da0891bea55ade5f69d9803d33480c3a2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6001cbec1488942a4856dca53c74adc0d5032df4ca5a58c00954f9bb0c364cb2",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2012-09-23T09:33:42Z",
    "title_canon_sha256": "88163f5768dc257562a99dd36b4744ec7e6f06cf6bc263d35856ba1906e1748a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.5043",
    "kind": "arxiv",
    "version": 2
  }
}