Pith Number

pith:4CGVZ225

pith:2009:4CGVZ225ZZBA6AXZMCFFKZL5SG

not attested not anchored not stored refs pending

Polarizations and symplectic isotopies

Emmanuel Opshtein

arxiv:0911.3601 v4 · 2009-11-18 · math.SG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4CGVZ225ZZBA6AXZMCFFKZL5SG}

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	2026-05-18T04:34:27.898629Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e08d5ceb5dce420f02f9608a55657d91b378280a0defaa289b245fcd6fd4ff35

Aliases

arxiv: 0911.3601 · arxiv_version: 0911.3601v4 · doi: 10.48550/arxiv.0911.3601 · pith_short_12: 4CGVZ225ZZBA · pith_short_16: 4CGVZ225ZZBA6AXZ · pith_short_8: 4CGVZ225

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/4CGVZ225ZZBA6AXZMCFFKZL5SG \
  | 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: e08d5ceb5dce420f02f9608a55657d91b378280a0defaa289b245fcd6fd4ff35

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "368e5c6d4538f51198cac18245db15d22ec88f8f339f112f9dafe800c491fc52",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SG",
    "submitted_at": "2009-11-18T17:01:41Z",
    "title_canon_sha256": "b37c2e28ef687340a0f8cc0a0ef76712049804682bf716cd3b24ff3dce70d9c7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0911.3601",
    "kind": "arxiv",
    "version": 4
  }
}