Pith Number

pith:3I4JITXP

pith:2011:3I4JITXP7FZOPXDWZJEXNUDDYI

not attested not anchored not stored refs pending

The family index theorem and bifurcation of solutions of nonlinear elliptic bvp

Jacobo Pejsachowicz

arxiv:1107.1727 v3 · 2011-07-08 · math.AP · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3I4JITXP7FZOPXDWZJEXNUDDYI}

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	2026-05-18T04:03:43.080685Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

da38944eeff972e7dc76ca4976d063c234be79f1b9455a9562d8d27e03530b6e

Aliases

arxiv: 1107.1727 · arxiv_version: 1107.1727v3 · doi: 10.48550/arxiv.1107.1727 · pith_short_12: 3I4JITXP7FZO · pith_short_16: 3I4JITXP7FZOPXDW · pith_short_8: 3I4JITXP

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/3I4JITXP7FZOPXDWZJEXNUDDYI \
  | 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: da38944eeff972e7dc76ca4976d063c234be79f1b9455a9562d8d27e03530b6e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0874f475cf55eeedf0688654cbaa03d3c560841dda720a83655fae347bb9494f",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-07-08T20:22:17Z",
    "title_canon_sha256": "78798a37bd0799c935e54180abac3d64d23d24ab2f99af9bc5ced4d75de3d116"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.1727",
    "kind": "arxiv",
    "version": 3
  }
}