Pith Number

pith:MMNQD6MC

pith:2015:MMNQD6MC3BV2TQKQWXQMPQ72WY

not attested not anchored not stored refs pending

Blow-up solutions for two coupled Gross-Pitaevskii equations with attractive interactions

Huan-Song Zhou, Xiaoyu Zeng, Yujin Guo

arxiv:1508.03718 v3 · 2015-08-15 · 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{MMNQD6MC3BV2TQKQWXQMPQ72WY}

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	2026-05-18T00:46:04.675163Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

631b01f982d86ba9c150b5e0c7c3fab61f8e03544f47ab320444e1d6e7205afd

Aliases

arxiv: 1508.03718 · arxiv_version: 1508.03718v3 · doi: 10.48550/arxiv.1508.03718 · pith_short_12: MMNQD6MC3BV2 · pith_short_16: MMNQD6MC3BV2TQKQ · pith_short_8: MMNQD6MC

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/MMNQD6MC3BV2TQKQWXQMPQ72WY \
  | 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: 631b01f982d86ba9c150b5e0c7c3fab61f8e03544f47ab320444e1d6e7205afd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b68f03df5061512a705360176ce1635a9a8de7a67623300ac4606748ea547674",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-08-15T10:02:48Z",
    "title_canon_sha256": "d1afe885d173f1d244dfce4ff211693c745c7d4a98f795799e2dd3643fdec9a5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.03718",
    "kind": "arxiv",
    "version": 3
  }
}