Pith Number

pith:HGAYLXRP

pith:2012:HGAYLXRPXKUZIQ32OKXXD2BUA5

not attested not anchored not stored refs pending

Global dynamics below the ground state energy for the Zakharov system in the 3D radial case

Kenji Nakanishi, Shuxia Wang, Zihua Guo

arxiv:1206.2457 v1 · 2012-06-12 · 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{HGAYLXRPXKUZIQ32OKXXD2BUA5}

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	2026-05-18T03:53:44.362456Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

398185de2fbaa994437a72af71e834077e4e4b0a30bcc01a50304b54e207cccf

Aliases

arxiv: 1206.2457 · arxiv_version: 1206.2457v1 · doi: 10.48550/arxiv.1206.2457 · pith_short_12: HGAYLXRPXKUZ · pith_short_16: HGAYLXRPXKUZIQ32 · pith_short_8: HGAYLXRP

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/HGAYLXRPXKUZIQ32OKXXD2BUA5 \
  | 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: 398185de2fbaa994437a72af71e834077e4e4b0a30bcc01a50304b54e207cccf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d8bd369cc9683cc15c0512c234a7e8fec922ced86b6096ad03fe5eb930ce9eac",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-06-12T08:30:01Z",
    "title_canon_sha256": "c9df553eae8e75a788166c8a23c072055f617c0d9f154edc00337362dd5543ed"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.2457",
    "kind": "arxiv",
    "version": 1
  }
}