Pith Number

pith:N3VA5TRM

pith:2007:N3VA5TRM4YKIUXF33QVUMF2QFR

not attested not anchored not stored refs pending

Approximation of definable sets by compact families, and upper bounds on homotopy and homology

Andrei Gabrielov, Nicolai Vorobjov

arxiv:0710.3028 v1 · 2007-10-16 · math.AG · math.LO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{N3VA5TRM4YKIUXF33QVUMF2QFR}

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	2026-05-18T02:58:12.179009Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6eea0ece2ce6148a5cbbdc2b4617502c5ea15a904c1ab05063bb23125423f5b7

Aliases

arxiv: 0710.3028 · arxiv_version: 0710.3028v1 · doi: 10.48550/arxiv.0710.3028 · pith_short_12: N3VA5TRM4YKI · pith_short_16: N3VA5TRM4YKIUXF3 · pith_short_8: N3VA5TRM

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/N3VA5TRM4YKIUXF33QVUMF2QFR \
  | 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: 6eea0ece2ce6148a5cbbdc2b4617502c5ea15a904c1ab05063bb23125423f5b7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cc72d2ca3de7a4c379ab336c420e43446add35d9fac110a7a2704cd0195e17c3",
    "cross_cats_sorted": [
      "math.LO"
    ],
    "license": "",
    "primary_cat": "math.AG",
    "submitted_at": "2007-10-16T12:01:22Z",
    "title_canon_sha256": "6dfdd37f84bbe21c68615663f6ca63a8b6bf375a28470654fe0b5f5cc392b6ec"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0710.3028",
    "kind": "arxiv",
    "version": 1
  }
}