{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:GFGG5OQ6CH7SIGMWGIWK2D7ITT","short_pith_number":"pith:GFGG5OQ6","canonical_record":{"source":{"id":"1606.07756","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-06-24T16:40:01Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"baf722f3e58ed4a0a6bc7b881029ae98ca7cfeb3870ca6c9466916238acdac9f","abstract_canon_sha256":"0f681a18e915e0b5d47800efc1547915621e681e2a499ab18a3ae5eeaed1295b"},"schema_version":"1.0"},"canonical_sha256":"314c6eba1e11ff241996322cad0fe89cf88fa5e3cfe2dcadb41bf4a614a7a096","source":{"kind":"arxiv","id":"1606.07756","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.07756","created_at":"2026-05-18T00:55:13Z"},{"alias_kind":"arxiv_version","alias_value":"1606.07756v1","created_at":"2026-05-18T00:55:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.07756","created_at":"2026-05-18T00:55:13Z"},{"alias_kind":"pith_short_12","alias_value":"GFGG5OQ6CH7S","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GFGG5OQ6CH7SIGMW","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GFGG5OQ6","created_at":"2026-05-18T12:30:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:GFGG5OQ6CH7SIGMWGIWK2D7ITT","target":"record","payload":{"canonical_record":{"source":{"id":"1606.07756","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-06-24T16:40:01Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"baf722f3e58ed4a0a6bc7b881029ae98ca7cfeb3870ca6c9466916238acdac9f","abstract_canon_sha256":"0f681a18e915e0b5d47800efc1547915621e681e2a499ab18a3ae5eeaed1295b"},"schema_version":"1.0"},"canonical_sha256":"314c6eba1e11ff241996322cad0fe89cf88fa5e3cfe2dcadb41bf4a614a7a096","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:55:13.453726Z","signature_b64":"4MWCOqJAHwCmC+AbLcDfMLnABuoozSVKU/FPvdj0jXdL2qebiA0AX9Fc8/NM3pBNLwNR3p5CLgdU62wD9A3jAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"314c6eba1e11ff241996322cad0fe89cf88fa5e3cfe2dcadb41bf4a614a7a096","last_reissued_at":"2026-05-18T00:55:13.453208Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:55:13.453208Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.07756","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":"2026-05-18T00:55:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"brwaePyVMs4jrYP2WUWURDCyRKov5PudoL18Zv/P08DSyiXddo6gWbpZcXTO1i9YuMiC0ASnMrXkulPIIAGEAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T06:12:47.568488Z"},"content_sha256":"3b5c1fa36a0257941801ad011056ab7711330a0588d0030e5c544713075f57f2","schema_version":"1.0","event_id":"sha256:3b5c1fa36a0257941801ad011056ab7711330a0588d0030e5c544713075f57f2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:GFGG5OQ6CH7SIGMWGIWK2D7ITT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Anisotropic Long-Range Spin Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"cond-mat.stat-mech","authors_text":"Andrea Trombettoni, Nicol\\`o Defenu, Stefano Ruffo","submitted_at":"2016-06-24T16:40:01Z","abstract_excerpt":"We consider anisotropic long-range interacting spin systems in $d$ dimensions. The interaction between the spins decays with the distance as a power law with different exponents in different directions: we consider an exponent $d_{1}+\\sigma_1$ in $d_1$ directions and another exponent $d_{2}+\\sigma_2$ in the remaining $d_2\\equiv d-d_1$ ones. We introduce a low energy effective action with non analytic power of the momenta. As a function of the two exponents $\\sigma_1$ and $\\sigma_2$ we show the system to have three different regimes, two where it is actually anisotropic and one where the isotro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.07756","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":"2026-05-18T00:55:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Jx82X49DaVOW/ZRPFfe4U7j/8zOBjnOD+yj4CSb6dfBexI6zPJxHVmCkoRLYBiofyAgMy3786i2XwEHWVokfAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T06:12:47.569164Z"},"content_sha256":"1983ef0ecdcab26be27bb6d07504a3f6a06bfe95df8986903e68709fa505da81","schema_version":"1.0","event_id":"sha256:1983ef0ecdcab26be27bb6d07504a3f6a06bfe95df8986903e68709fa505da81"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GFGG5OQ6CH7SIGMWGIWK2D7ITT/bundle.json","state_url":"https://pith.science/pith/GFGG5OQ6CH7SIGMWGIWK2D7ITT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GFGG5OQ6CH7SIGMWGIWK2D7ITT/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":"2026-06-07T06:12:47Z","links":{"resolver":"https://pith.science/pith/GFGG5OQ6CH7SIGMWGIWK2D7ITT","bundle":"https://pith.science/pith/GFGG5OQ6CH7SIGMWGIWK2D7ITT/bundle.json","state":"https://pith.science/pith/GFGG5OQ6CH7SIGMWGIWK2D7ITT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GFGG5OQ6CH7SIGMWGIWK2D7ITT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:GFGG5OQ6CH7SIGMWGIWK2D7ITT","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":"0f681a18e915e0b5d47800efc1547915621e681e2a499ab18a3ae5eeaed1295b","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-06-24T16:40:01Z","title_canon_sha256":"baf722f3e58ed4a0a6bc7b881029ae98ca7cfeb3870ca6c9466916238acdac9f"},"schema_version":"1.0","source":{"id":"1606.07756","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.07756","created_at":"2026-05-18T00:55:13Z"},{"alias_kind":"arxiv_version","alias_value":"1606.07756v1","created_at":"2026-05-18T00:55:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.07756","created_at":"2026-05-18T00:55:13Z"},{"alias_kind":"pith_short_12","alias_value":"GFGG5OQ6CH7S","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GFGG5OQ6CH7SIGMW","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GFGG5OQ6","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:1983ef0ecdcab26be27bb6d07504a3f6a06bfe95df8986903e68709fa505da81","target":"graph","created_at":"2026-05-18T00:55:13Z","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":"We consider anisotropic long-range interacting spin systems in $d$ dimensions. The interaction between the spins decays with the distance as a power law with different exponents in different directions: we consider an exponent $d_{1}+\\sigma_1$ in $d_1$ directions and another exponent $d_{2}+\\sigma_2$ in the remaining $d_2\\equiv d-d_1$ ones. We introduce a low energy effective action with non analytic power of the momenta. As a function of the two exponents $\\sigma_1$ and $\\sigma_2$ we show the system to have three different regimes, two where it is actually anisotropic and one where the isotro","authors_text":"Andrea Trombettoni, Nicol\\`o Defenu, Stefano Ruffo","cross_cats":["hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-06-24T16:40:01Z","title":"Anisotropic Long-Range Spin Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.07756","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":"sha256:3b5c1fa36a0257941801ad011056ab7711330a0588d0030e5c544713075f57f2","target":"record","created_at":"2026-05-18T00:55:13Z","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":"0f681a18e915e0b5d47800efc1547915621e681e2a499ab18a3ae5eeaed1295b","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-06-24T16:40:01Z","title_canon_sha256":"baf722f3e58ed4a0a6bc7b881029ae98ca7cfeb3870ca6c9466916238acdac9f"},"schema_version":"1.0","source":{"id":"1606.07756","kind":"arxiv","version":1}},"canonical_sha256":"314c6eba1e11ff241996322cad0fe89cf88fa5e3cfe2dcadb41bf4a614a7a096","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"314c6eba1e11ff241996322cad0fe89cf88fa5e3cfe2dcadb41bf4a614a7a096","first_computed_at":"2026-05-18T00:55:13.453208Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:55:13.453208Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4MWCOqJAHwCmC+AbLcDfMLnABuoozSVKU/FPvdj0jXdL2qebiA0AX9Fc8/NM3pBNLwNR3p5CLgdU62wD9A3jAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:55:13.453726Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.07756","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3b5c1fa36a0257941801ad011056ab7711330a0588d0030e5c544713075f57f2","sha256:1983ef0ecdcab26be27bb6d07504a3f6a06bfe95df8986903e68709fa505da81"],"state_sha256":"0063a3c39a574d9ecfdcd489bd9b4b6f004c4108bfb3d1956782a4b52b07f7b8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DVkRHYNNO0OAMHAuJPwnHkhoFHib99nckpuJE5kT3yTkrij1GvSBWpLTw4c16nZbJLvNn8ZvXQ5kaU45XeW6Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T06:12:47.572782Z","bundle_sha256":"607a97f3fd20a2b3aa8a9e40381777eb636edb6feb539cb17863a11718998629"}}