Pith Number

pith:M4PSN3XO

pith:2009:M4PSN3XOXCPCNT7NKDDWW2GXPD

not attested not anchored not stored refs pending

Parallel submanifolds with an intrinsic product structure

Tillmann Jentsch

arxiv:0911.3857 v3 · 2009-11-19 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{M4PSN3XOXCPCNT7NKDDWW2GXPD}

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	2026-05-18T03:54:06.330890Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

671f26eeeeb89e26cfed50c76b68d778ceb3d15b12066fc6386c3a3c3e9709b0

Aliases

arxiv: 0911.3857 · arxiv_version: 0911.3857v3 · doi: 10.48550/arxiv.0911.3857 · pith_short_12: M4PSN3XOXCPC · pith_short_16: M4PSN3XOXCPCNT7N · pith_short_8: M4PSN3XO

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/M4PSN3XOXCPCNT7NKDDWW2GXPD \
  | 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: 671f26eeeeb89e26cfed50c76b68d778ceb3d15b12066fc6386c3a3c3e9709b0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7b0f4efb588921a0b6ae869187f8430f7eebfa1b7dead925d0c86122fc652bc4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2009-11-19T17:58:46Z",
    "title_canon_sha256": "c2011a795c4fc2dad85159e53a8eb3858da71daea4108f50b491e936019223a4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0911.3857",
    "kind": "arxiv",
    "version": 3
  }
}