Pith Number

pith:GIXD3U74

pith:2011:GIXD3U74X7OCCIEKQQMJ5NFTBN

not attested not anchored not stored refs pending

A Homotopy-like Class Invariant for Sub-manifolds of Punctured Euclidean Spaces

Maxim Likhachev, Subhrajit Bhattacharya, Vijay Kumar

arxiv:1103.2488 v1 · 2011-03-13 · math.DG · math.AT · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GIXD3U74X7OCCIEKQQMJ5NFTBN}

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	2026-05-18T04:26:55.209178Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

322e3dd3fcbfdc21208a84189eb4b30b45c2bb02127e915de64a0bedc1205a5f

Aliases

arxiv: 1103.2488 · arxiv_version: 1103.2488v1 · doi: 10.48550/arxiv.1103.2488 · pith_short_12: GIXD3U74X7OC · pith_short_16: GIXD3U74X7OCCIEK · pith_short_8: GIXD3U74

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/GIXD3U74X7OCCIEKQQMJ5NFTBN \
  | 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: 322e3dd3fcbfdc21208a84189eb4b30b45c2bb02127e915de64a0bedc1205a5f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "df2063b382a97685a37ec125085e4f68314e9be6941659e166a910ac3541b8e9",
    "cross_cats_sorted": [
      "math.AT",
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2011-03-13T01:36:25Z",
    "title_canon_sha256": "ceefbbad9293b2f42b1bb57fdf95d18e0aa4442baf6978fab485d39a00a8ea64"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.2488",
    "kind": "arxiv",
    "version": 1
  }
}