Pith Number

pith:YLUMEI6X

pith:2012:YLUMEI6XXWJEZTZBAK7VW4M77C

not attested not anchored not stored refs pending

A modification of the Hodge star operator on manifolds with boundary

Ryszard L. Rubinsztein

arxiv:1212.0713 v1 · 2012-12-04 · math.SG · 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{YLUMEI6XXWJEZTZBAK7VW4M77C}

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	2026-05-18T01:52:47.924457Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c2e8c223d7bd924ccf2102bf5b719ff89cf31c02fd4f7fe01c5e0c7809f96bc3

Aliases

arxiv: 1212.0713 · arxiv_version: 1212.0713v1 · doi: 10.48550/arxiv.1212.0713 · pith_short_12: YLUMEI6XXWJE · pith_short_16: YLUMEI6XXWJEZTZB · pith_short_8: YLUMEI6X

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/YLUMEI6XXWJEZTZBAK7VW4M77C \
  | 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: c2e8c223d7bd924ccf2102bf5b719ff89cf31c02fd4f7fe01c5e0c7809f96bc3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3073f85b0e3af3c32e0605add5215573f7b08ab191175050394810d6b0cd82ab",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SG",
    "submitted_at": "2012-12-04T13:16:12Z",
    "title_canon_sha256": "f35d8e0348c3c8a1e77f0c5af56348ea464e2dedf133de0b2cdd93b7e0af5eab"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.0713",
    "kind": "arxiv",
    "version": 1
  }
}