Pith Number

pith:SA2GU5KC

pith:2012:SA2GU5KCMVBR7SAP7JR6CI6WJK

not attested not anchored not stored refs pending

Discontinuous symplectic capacities

Fabian Ziltener, Kai Zehmisch

arxiv:1208.6000 v4 · 2012-08-29 · 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{SA2GU5KCMVBR7SAP7JR6CI6WJK}

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	2026-05-18T02:52:12.895681Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

90346a754265431fc80ffa63e123d64ab330fe6aad69176b08d995b5d276ff00

Aliases

arxiv: 1208.6000 · arxiv_version: 1208.6000v4 · doi: 10.48550/arxiv.1208.6000 · pith_short_12: SA2GU5KCMVBR · pith_short_16: SA2GU5KCMVBR7SAP · pith_short_8: SA2GU5KC

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/SA2GU5KCMVBR7SAP7JR6CI6WJK \
  | 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: 90346a754265431fc80ffa63e123d64ab330fe6aad69176b08d995b5d276ff00

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "83dac2f3d134dc9248cbbcfec9f256edd27e07c694b6de355522f1208282ac0c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SG",
    "submitted_at": "2012-08-29T19:33:18Z",
    "title_canon_sha256": "8a81be4e888e7d03eeffbd2d9277dcf78801186104882d55a9fc3199e832337f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.6000",
    "kind": "arxiv",
    "version": 4
  }
}