Pith Number

pith:ZH2ZI76A

pith:2005:ZH2ZI76AYHPKXE2GFKBDQEKYA5

not attested not anchored not stored refs pending

Holomorphic injectivity and the Hopf map

Frederico Xavier, Scott Nollet

arxiv:math/0501196 v1 · 2005-01-13 · math.AG · 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{ZH2ZI76AYHPKXE2GFKBDQEKYA5}

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	2026-05-18T03:40:26.048227Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c9f5947fc0c1deab93462a82381158077d893097c1db0ad095b9d6249bb0f984

Aliases

arxiv: math/0501196 · arxiv_version: math/0501196v1 · doi: 10.48550/arxiv.math/0501196 · pith_short_12: ZH2ZI76AYHPK · pith_short_16: ZH2ZI76AYHPKXE2G · pith_short_8: ZH2ZI76A

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/ZH2ZI76AYHPKXE2GFKBDQEKYA5 \
  | 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: c9f5947fc0c1deab93462a82381158077d893097c1db0ad095b9d6249bb0f984

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "63267dac001d8f505945c093281a84336a7536e1bfdee02b79db171856c32aab",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "",
    "primary_cat": "math.AG",
    "submitted_at": "2005-01-13T08:36:30Z",
    "title_canon_sha256": "1daecd8e1ab2bc13552554d928d247ebaa49dd9fd52e7ba051225f3b9d3c5d54"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0501196",
    "kind": "arxiv",
    "version": 1
  }
}