{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:UM36IVI4RU5PETWZIWSRJWA5BE","short_pith_number":"pith:UM36IVI4","canonical_record":{"source":{"id":"1708.09795","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-08-31T16:18:01Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"5ec3d886c8e8924b7c94240a321beede4f241b04e2a4283bb1aa32860a2996be","abstract_canon_sha256":"38f71021fdc9556f9421818ae453a67b262dd78c5543fbfbc8359db907381669"},"schema_version":"1.0"},"canonical_sha256":"a337e4551c8d3af24ed945a514d81d090694f4a0ec6c0f5796587e40b4fa6f16","source":{"kind":"arxiv","id":"1708.09795","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.09795","created_at":"2026-05-18T00:22:58Z"},{"alias_kind":"arxiv_version","alias_value":"1708.09795v2","created_at":"2026-05-18T00:22:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.09795","created_at":"2026-05-18T00:22:58Z"},{"alias_kind":"pith_short_12","alias_value":"UM36IVI4RU5P","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"UM36IVI4RU5PETWZ","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"UM36IVI4","created_at":"2026-05-18T12:31:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:UM36IVI4RU5PETWZIWSRJWA5BE","target":"record","payload":{"canonical_record":{"source":{"id":"1708.09795","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-08-31T16:18:01Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"5ec3d886c8e8924b7c94240a321beede4f241b04e2a4283bb1aa32860a2996be","abstract_canon_sha256":"38f71021fdc9556f9421818ae453a67b262dd78c5543fbfbc8359db907381669"},"schema_version":"1.0"},"canonical_sha256":"a337e4551c8d3af24ed945a514d81d090694f4a0ec6c0f5796587e40b4fa6f16","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:58.838692Z","signature_b64":"l/l+zBXfsjY2JiYIFkgQaTSInWIK5+sBmvpS3uglZX+sbUb/wGWLz2XT0E7vE0xmjxaOWM1/w3DKJp/n/MBuDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a337e4551c8d3af24ed945a514d81d090694f4a0ec6c0f5796587e40b4fa6f16","last_reissued_at":"2026-05-18T00:22:58.838217Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:58.838217Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.09795","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:22:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wi5lYuRGL6TjBmc4yHX/iVd0TqfOr9fdgb5jqoQQo8co1tar/kcj55hXcvzTbztiph5/+tOuCMg9g1sB5/1qBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T04:36:05.473445Z"},"content_sha256":"641ba581bc7249c9c28de95ec8c8da4a99872f71b738d5610cb20c14e7b97fd2","schema_version":"1.0","event_id":"sha256:641ba581bc7249c9c28de95ec8c8da4a99872f71b738d5610cb20c14e7b97fd2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:UM36IVI4RU5PETWZIWSRJWA5BE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multi-critical $\\square^k$ scalar theories: A perturbative RG approach with $\\epsilon$-expansion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"hep-th","authors_text":"Gian Paolo Vacca, Mahmoud Safari","submitted_at":"2017-08-31T16:18:01Z","abstract_excerpt":"We employ perturbative RG and $\\epsilon$-expansion to study multi-critical single-scalar field theories with higher derivative kinetic terms of the form $\\phi(-\\Box)^k\\phi$. We focus on those with a $\\mathbb{Z}_2$-symmetric critical point which are characterized by an upper critical dimension $d_c=2 n k/(n-1)$ accumulating at even integers. We distinguish two types of theories depending on whether or not the numbers $k$ and $n-1$ are relatively prime. When they are, the theory admits a local potential approximation. In this case we present the beta functional of the potential and use this to c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.09795","kind":"arxiv","version":2},"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":"2026-05-18T00:22:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QOB06BfGNhzEy6BTVqgDk12H+fXGbqb3yTtSPsJRxJ71RUbVZzYTddBRMewLimwgWZNmJVxQOWRAQsVCQxABBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T04:36:05.473855Z"},"content_sha256":"6b53a07c226bec561978c1f1b43b98ec83339757ac5728c969b14f01af5f5099","schema_version":"1.0","event_id":"sha256:6b53a07c226bec561978c1f1b43b98ec83339757ac5728c969b14f01af5f5099"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UM36IVI4RU5PETWZIWSRJWA5BE/bundle.json","state_url":"https://pith.science/pith/UM36IVI4RU5PETWZIWSRJWA5BE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UM36IVI4RU5PETWZIWSRJWA5BE/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":"2026-05-22T04:36:05Z","links":{"resolver":"https://pith.science/pith/UM36IVI4RU5PETWZIWSRJWA5BE","bundle":"https://pith.science/pith/UM36IVI4RU5PETWZIWSRJWA5BE/bundle.json","state":"https://pith.science/pith/UM36IVI4RU5PETWZIWSRJWA5BE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UM36IVI4RU5PETWZIWSRJWA5BE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:UM36IVI4RU5PETWZIWSRJWA5BE","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":"38f71021fdc9556f9421818ae453a67b262dd78c5543fbfbc8359db907381669","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-08-31T16:18:01Z","title_canon_sha256":"5ec3d886c8e8924b7c94240a321beede4f241b04e2a4283bb1aa32860a2996be"},"schema_version":"1.0","source":{"id":"1708.09795","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.09795","created_at":"2026-05-18T00:22:58Z"},{"alias_kind":"arxiv_version","alias_value":"1708.09795v2","created_at":"2026-05-18T00:22:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.09795","created_at":"2026-05-18T00:22:58Z"},{"alias_kind":"pith_short_12","alias_value":"UM36IVI4RU5P","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"UM36IVI4RU5PETWZ","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"UM36IVI4","created_at":"2026-05-18T12:31:46Z"}],"graph_snapshots":[{"event_id":"sha256:6b53a07c226bec561978c1f1b43b98ec83339757ac5728c969b14f01af5f5099","target":"graph","created_at":"2026-05-18T00:22:58Z","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 employ perturbative RG and $\\epsilon$-expansion to study multi-critical single-scalar field theories with higher derivative kinetic terms of the form $\\phi(-\\Box)^k\\phi$. We focus on those with a $\\mathbb{Z}_2$-symmetric critical point which are characterized by an upper critical dimension $d_c=2 n k/(n-1)$ accumulating at even integers. We distinguish two types of theories depending on whether or not the numbers $k$ and $n-1$ are relatively prime. When they are, the theory admits a local potential approximation. In this case we present the beta functional of the potential and use this to c","authors_text":"Gian Paolo Vacca, Mahmoud Safari","cross_cats":["cond-mat.stat-mech"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-08-31T16:18:01Z","title":"Multi-critical $\\square^k$ scalar theories: A perturbative RG approach with $\\epsilon$-expansion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.09795","kind":"arxiv","version":2},"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":"sha256:641ba581bc7249c9c28de95ec8c8da4a99872f71b738d5610cb20c14e7b97fd2","target":"record","created_at":"2026-05-18T00:22:58Z","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":"38f71021fdc9556f9421818ae453a67b262dd78c5543fbfbc8359db907381669","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-08-31T16:18:01Z","title_canon_sha256":"5ec3d886c8e8924b7c94240a321beede4f241b04e2a4283bb1aa32860a2996be"},"schema_version":"1.0","source":{"id":"1708.09795","kind":"arxiv","version":2}},"canonical_sha256":"a337e4551c8d3af24ed945a514d81d090694f4a0ec6c0f5796587e40b4fa6f16","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a337e4551c8d3af24ed945a514d81d090694f4a0ec6c0f5796587e40b4fa6f16","first_computed_at":"2026-05-18T00:22:58.838217Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:58.838217Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"l/l+zBXfsjY2JiYIFkgQaTSInWIK5+sBmvpS3uglZX+sbUb/wGWLz2XT0E7vE0xmjxaOWM1/w3DKJp/n/MBuDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:58.838692Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.09795","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:641ba581bc7249c9c28de95ec8c8da4a99872f71b738d5610cb20c14e7b97fd2","sha256:6b53a07c226bec561978c1f1b43b98ec83339757ac5728c969b14f01af5f5099"],"state_sha256":"c849a20d97275c35f5a4b193377607e9495b22b0aa1d338e37c19c36c771909a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A/1rSOlWXr8GMJWQqxVdZaDRLe7wIiSyoEKNZhcYP+syyhnSBvcDJqu+oGPIukJLrFKiZwoV2imko1YR2oR5Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T04:36:05.476157Z","bundle_sha256":"e16df05fc238a53fd8695f8565e60b8e59ec94718fb7efa73df683c27f99318d"}}