Pith Number

pith:P47PU55L

pith:2007:P47PU55LO7CUYY5UEXQXNNJZ7H

not attested not anchored not stored refs pending

Invertible harmonic mappings, beyond Kneser

Giovanni Alessandrini, Vincenzo Nesi

arxiv:0712.3840 v2 · 2007-12-22 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{P47PU55LO7CUYY5UEXQXNNJZ7H}

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	2026-05-18T04:36:50.555739Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7f3efa77ab77c54c63b425e176b539f9e95d404b5c98bc4a2b76aead5063328d

Aliases

arxiv: 0712.3840 · arxiv_version: 0712.3840v2 · doi: 10.48550/arxiv.0712.3840 · pith_short_12: P47PU55LO7CU · pith_short_16: P47PU55LO7CUYY5U · pith_short_8: P47PU55L

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/P47PU55LO7CUYY5UEXQXNNJZ7H \
  | 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: 7f3efa77ab77c54c63b425e176b539f9e95d404b5c98bc4a2b76aead5063328d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "69b851d747d09e3d6a1fa9210d0648ac2eb5abe16ba7108931434eb6ba87cd09",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.AP",
    "submitted_at": "2007-12-22T08:39:15Z",
    "title_canon_sha256": "c8f2c280e5a5b0f1e9ce6bc26384c35af55d909b1f6909f2dc65cef169371a55"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0712.3840",
    "kind": "arxiv",
    "version": 2
  }
}