{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:WYSPW75PWQFRVGBMXJYMTVXWJW","short_pith_number":"pith:WYSPW75P","canonical_record":{"source":{"id":"1303.4521","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-03-19T09:21:59Z","cross_cats_sorted":[],"title_canon_sha256":"9b0e3a60544598b799959d562c5234e27472efe0305d5d98a0dcd5ede539751e","abstract_canon_sha256":"e14030d60e27dfe97672d9ff598ff95ff9f38f9e2b318ae08192b95367df6b9a"},"schema_version":"1.0"},"canonical_sha256":"b624fb7fafb40b1a982cba70c9d6f64d817515b413958905b5ad6cacc99eaffc","source":{"kind":"arxiv","id":"1303.4521","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.4521","created_at":"2026-05-18T03:30:26Z"},{"alias_kind":"arxiv_version","alias_value":"1303.4521v1","created_at":"2026-05-18T03:30:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.4521","created_at":"2026-05-18T03:30:26Z"},{"alias_kind":"pith_short_12","alias_value":"WYSPW75PWQFR","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"WYSPW75PWQFRVGBM","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"WYSPW75P","created_at":"2026-05-18T12:28:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:WYSPW75PWQFRVGBMXJYMTVXWJW","target":"record","payload":{"canonical_record":{"source":{"id":"1303.4521","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-03-19T09:21:59Z","cross_cats_sorted":[],"title_canon_sha256":"9b0e3a60544598b799959d562c5234e27472efe0305d5d98a0dcd5ede539751e","abstract_canon_sha256":"e14030d60e27dfe97672d9ff598ff95ff9f38f9e2b318ae08192b95367df6b9a"},"schema_version":"1.0"},"canonical_sha256":"b624fb7fafb40b1a982cba70c9d6f64d817515b413958905b5ad6cacc99eaffc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:30:26.900460Z","signature_b64":"Wxl/WG8H7g+wXfpUXyblbPWyJkhlOnN0U4mtxZMeWlq+gZ/RAhM1cDwwBrGZL08fNueQtPAkCOl0QnGiFrP7AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b624fb7fafb40b1a982cba70c9d6f64d817515b413958905b5ad6cacc99eaffc","last_reissued_at":"2026-05-18T03:30:26.899722Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:30:26.899722Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1303.4521","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:30:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AaQu+G1Xbs6DlKgS1zWUcZEEgXxNwi2ZGnluSB/lATZBg2hQdI4/2psOw+/YNb411za3SPQEgslV7LaZczMRDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T11:39:04.585899Z"},"content_sha256":"714b56626156d68fe13dd3d3d26e84932193538af5ce330dd6aed1438defa86e","schema_version":"1.0","event_id":"sha256:714b56626156d68fe13dd3d3d26e84932193538af5ce330dd6aed1438defa86e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:WYSPW75PWQFRVGBMXJYMTVXWJW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Minimal energy solutions for repulsive nonlinear Schr\\\"odinger systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Rainer Mandel","submitted_at":"2013-03-19T09:21:59Z","abstract_excerpt":"In this paper we establish existence and nonexistence results concerning fully nontrivial minimal energy solutions of the nonlinear Schr\\\"odinger system\n  \\begin{align*}\n  \\begin{gathered}\n  -\\Delta u + \\, u = |u|^{2q-2}u + b|u|^{q-2}u|v|^q \\quad\\text{in}\\R^n,\n  -\\Delta v + \\omega^2 v = |v|^{2q-2}v + b|u|^q|v|^{q-2}v\\quad\\text{in}\\R^n.\n  \\end{gathered}\n  \\end{align*}\n  We consider the repulsive case $b<0$ and assume that the exponent $q$ satisfies $1<q<\\frac{n}{n-2}$ in case $n\\geq 3$ and $1<q<\\infty$ in case $n=1$ or $n=2$. For space dimensions $n\\geq 2$ and arbitrary $b<0$ we prove the exist"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.4521","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:30:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WnFd5ECbgJCibiYNoU1jGkpDAlUHb+xYiDqA3TlF1GbwgkQu/yOnj9q7btG0JxB0UlFiM6Un4AynVi4MQpOVAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T11:39:04.586247Z"},"content_sha256":"74ca47892d6c61e953aab59bd3648a1928eebb0374c6e9d450a3d0040c924e0f","schema_version":"1.0","event_id":"sha256:74ca47892d6c61e953aab59bd3648a1928eebb0374c6e9d450a3d0040c924e0f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WYSPW75PWQFRVGBMXJYMTVXWJW/bundle.json","state_url":"https://pith.science/pith/WYSPW75PWQFRVGBMXJYMTVXWJW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WYSPW75PWQFRVGBMXJYMTVXWJW/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-24T11:39:04Z","links":{"resolver":"https://pith.science/pith/WYSPW75PWQFRVGBMXJYMTVXWJW","bundle":"https://pith.science/pith/WYSPW75PWQFRVGBMXJYMTVXWJW/bundle.json","state":"https://pith.science/pith/WYSPW75PWQFRVGBMXJYMTVXWJW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WYSPW75PWQFRVGBMXJYMTVXWJW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:WYSPW75PWQFRVGBMXJYMTVXWJW","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"e14030d60e27dfe97672d9ff598ff95ff9f38f9e2b318ae08192b95367df6b9a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-03-19T09:21:59Z","title_canon_sha256":"9b0e3a60544598b799959d562c5234e27472efe0305d5d98a0dcd5ede539751e"},"schema_version":"1.0","source":{"id":"1303.4521","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.4521","created_at":"2026-05-18T03:30:26Z"},{"alias_kind":"arxiv_version","alias_value":"1303.4521v1","created_at":"2026-05-18T03:30:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.4521","created_at":"2026-05-18T03:30:26Z"},{"alias_kind":"pith_short_12","alias_value":"WYSPW75PWQFR","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"WYSPW75PWQFRVGBM","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"WYSPW75P","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:74ca47892d6c61e953aab59bd3648a1928eebb0374c6e9d450a3d0040c924e0f","target":"graph","created_at":"2026-05-18T03:30:26Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper we establish existence and nonexistence results concerning fully nontrivial minimal energy solutions of the nonlinear Schr\\\"odinger system\n  \\begin{align*}\n  \\begin{gathered}\n  -\\Delta u + \\, u = |u|^{2q-2}u + b|u|^{q-2}u|v|^q \\quad\\text{in}\\R^n,\n  -\\Delta v + \\omega^2 v = |v|^{2q-2}v + b|u|^q|v|^{q-2}v\\quad\\text{in}\\R^n.\n  \\end{gathered}\n  \\end{align*}\n  We consider the repulsive case $b<0$ and assume that the exponent $q$ satisfies $1<q<\\frac{n}{n-2}$ in case $n\\geq 3$ and $1<q<\\infty$ in case $n=1$ or $n=2$. For space dimensions $n\\geq 2$ and arbitrary $b<0$ we prove the exist","authors_text":"Rainer Mandel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-03-19T09:21:59Z","title":"Minimal energy solutions for repulsive nonlinear Schr\\\"odinger systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.4521","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:714b56626156d68fe13dd3d3d26e84932193538af5ce330dd6aed1438defa86e","target":"record","created_at":"2026-05-18T03:30:26Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"e14030d60e27dfe97672d9ff598ff95ff9f38f9e2b318ae08192b95367df6b9a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-03-19T09:21:59Z","title_canon_sha256":"9b0e3a60544598b799959d562c5234e27472efe0305d5d98a0dcd5ede539751e"},"schema_version":"1.0","source":{"id":"1303.4521","kind":"arxiv","version":1}},"canonical_sha256":"b624fb7fafb40b1a982cba70c9d6f64d817515b413958905b5ad6cacc99eaffc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b624fb7fafb40b1a982cba70c9d6f64d817515b413958905b5ad6cacc99eaffc","first_computed_at":"2026-05-18T03:30:26.899722Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:30:26.899722Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Wxl/WG8H7g+wXfpUXyblbPWyJkhlOnN0U4mtxZMeWlq+gZ/RAhM1cDwwBrGZL08fNueQtPAkCOl0QnGiFrP7AA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:30:26.900460Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.4521","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:714b56626156d68fe13dd3d3d26e84932193538af5ce330dd6aed1438defa86e","sha256:74ca47892d6c61e953aab59bd3648a1928eebb0374c6e9d450a3d0040c924e0f"],"state_sha256":"228cd222eec9f0ffbd2cd659a2ed841f3db6b9365e914b595e1961ddda346f0c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nhP3nlUw5Og8RjRDHd5OmGCdbR4PIU/wpYhSkno8Db6hXOTGQKMe693B8hbT+mHDfPXpYp3ygjrlQRNQu/6KAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T11:39:04.588473Z","bundle_sha256":"4d54d742ddbe08f46545717b20488543bf235106ab66b09462eeac4df5366f6d"}}