Pith Number

pith:R22V6Q2W

pith:2017:R22V6Q2W4P3UFUYFNVFQ334GF2

not attested not anchored not stored refs pending

A global bifurcation theorem for critical values of $C^1$ maps in Banach spaces

Julian Haddad, Pablo Amster, Pierluigi Benevieri

arxiv:1708.01340 v1 · 2017-08-04 · 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{R22V6Q2W4P3UFUYFNVFQ334GF2}

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	2026-05-18T00:38:37.630196Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8eb55f4356e3f742d3056d4b0def862eac33f8e476e711d2a0bb77c8fe0dbf23

Aliases

arxiv: 1708.01340 · arxiv_version: 1708.01340v1 · doi: 10.48550/arxiv.1708.01340 · pith_short_12: R22V6Q2W4P3U · pith_short_16: R22V6Q2W4P3UFUYF · pith_short_8: R22V6Q2W

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/R22V6Q2W4P3UFUYFNVFQ334GF2 \
  | 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: 8eb55f4356e3f742d3056d4b0def862eac33f8e476e711d2a0bb77c8fe0dbf23

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d608f57c58e243e435f0ba218c617216be6a0c79eb6329baf6447e95ceaa54de",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2017-08-04T00:43:45Z",
    "title_canon_sha256": "7073a176bcf56df0c2c61003e4c11855813233fd06e16e4b000a1c7165c27763"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1708.01340",
    "kind": "arxiv",
    "version": 1
  }
}