{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:VOQ3L4JG5OKE33KARNO3K2OZCB","short_pith_number":"pith:VOQ3L4JG","canonical_record":{"source":{"id":"1406.3626","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-06-13T20:00:01Z","cross_cats_sorted":[],"title_canon_sha256":"d182a708a340bbc75d6dc12f8e24578590d63a41ebdaf0cbad731d9f95cd40d9","abstract_canon_sha256":"9fabd880e53fdbfd4c6db08a10be0cfef378977f2e15680c75abc21cf2c97cda"},"schema_version":"1.0"},"canonical_sha256":"aba1b5f126eb944ded408b5db569d91077ecdf075d3a0cc20cbbff31de908106","source":{"kind":"arxiv","id":"1406.3626","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.3626","created_at":"2026-05-18T02:18:04Z"},{"alias_kind":"arxiv_version","alias_value":"1406.3626v2","created_at":"2026-05-18T02:18:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.3626","created_at":"2026-05-18T02:18:04Z"},{"alias_kind":"pith_short_12","alias_value":"VOQ3L4JG5OKE","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"VOQ3L4JG5OKE33KA","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"VOQ3L4JG","created_at":"2026-05-18T12:28:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:VOQ3L4JG5OKE33KARNO3K2OZCB","target":"record","payload":{"canonical_record":{"source":{"id":"1406.3626","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-06-13T20:00:01Z","cross_cats_sorted":[],"title_canon_sha256":"d182a708a340bbc75d6dc12f8e24578590d63a41ebdaf0cbad731d9f95cd40d9","abstract_canon_sha256":"9fabd880e53fdbfd4c6db08a10be0cfef378977f2e15680c75abc21cf2c97cda"},"schema_version":"1.0"},"canonical_sha256":"aba1b5f126eb944ded408b5db569d91077ecdf075d3a0cc20cbbff31de908106","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:04.259976Z","signature_b64":"8aPvjx3uP99k+2FJeLZ+cdIpgPBRnfMuCb728clYfcB00aCLhzhMDUz9k034UzRhE5GkpZO+FqS29mXAFWEvBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aba1b5f126eb944ded408b5db569d91077ecdf075d3a0cc20cbbff31de908106","last_reissued_at":"2026-05-18T02:18:04.259194Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:04.259194Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.3626","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":"2026-05-18T02:18:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CSPwTWIokUZUzaC0HCUo8jyyuaBuN/dM52RCnmAReK0IJ9ZudM/VW+0LYtkrkg3WodVXXud0n5RZfVHM4j3GCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T10:02:17.636671Z"},"content_sha256":"be737d6bae73b2242356149961580a77b73d866b5ce6b446d5e9251d570d0b3e","schema_version":"1.0","event_id":"sha256:be737d6bae73b2242356149961580a77b73d866b5ce6b446d5e9251d570d0b3e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:VOQ3L4JG5OKE33KARNO3K2OZCB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A challenge to the $a$-theorem in six dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Andreas Stergiou, Benjamin Grinstein, David Stone, Ming Zhong","submitted_at":"2014-06-13T20:00:01Z","abstract_excerpt":"The possibility of a strong $a$-theorem in six dimensions is examined in multi-flavor $\\phi^3$ theory. Contrary to the case in two and four dimensions, we find that in perturbation theory the relevant quantity $\\tilde{a}$ increases monotonically along flows away from the trivial fixed point. $\\tilde{a}$ is a natural extension of the coefficient $a$ of the Euler term in the trace anomaly, and it arises in any even spacetime dimension from an analysis based on Weyl consistency conditions. We also obtain the anomalous dimensions and beta functions of multi-flavor $\\phi^3$ theory to two loops. Our"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3626","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":"2026-05-18T02:18:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n9GFY3M180sIHnMaC2GEzHx/t3mQ9omFmacUpIYJUbD/mlQxiPXFFEy7p/a421vMxOf/m+30Z5IbUJ0/OmcFDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T10:02:17.637022Z"},"content_sha256":"4b2b9ee18907cb04cbe796daa73d88f25046c551583d6509f558f1a1fbecb09e","schema_version":"1.0","event_id":"sha256:4b2b9ee18907cb04cbe796daa73d88f25046c551583d6509f558f1a1fbecb09e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VOQ3L4JG5OKE33KARNO3K2OZCB/bundle.json","state_url":"https://pith.science/pith/VOQ3L4JG5OKE33KARNO3K2OZCB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VOQ3L4JG5OKE33KARNO3K2OZCB/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":"2026-05-28T10:02:17Z","links":{"resolver":"https://pith.science/pith/VOQ3L4JG5OKE33KARNO3K2OZCB","bundle":"https://pith.science/pith/VOQ3L4JG5OKE33KARNO3K2OZCB/bundle.json","state":"https://pith.science/pith/VOQ3L4JG5OKE33KARNO3K2OZCB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VOQ3L4JG5OKE33KARNO3K2OZCB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:VOQ3L4JG5OKE33KARNO3K2OZCB","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":"9fabd880e53fdbfd4c6db08a10be0cfef378977f2e15680c75abc21cf2c97cda","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-06-13T20:00:01Z","title_canon_sha256":"d182a708a340bbc75d6dc12f8e24578590d63a41ebdaf0cbad731d9f95cd40d9"},"schema_version":"1.0","source":{"id":"1406.3626","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.3626","created_at":"2026-05-18T02:18:04Z"},{"alias_kind":"arxiv_version","alias_value":"1406.3626v2","created_at":"2026-05-18T02:18:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.3626","created_at":"2026-05-18T02:18:04Z"},{"alias_kind":"pith_short_12","alias_value":"VOQ3L4JG5OKE","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"VOQ3L4JG5OKE33KA","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"VOQ3L4JG","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:4b2b9ee18907cb04cbe796daa73d88f25046c551583d6509f558f1a1fbecb09e","target":"graph","created_at":"2026-05-18T02:18:04Z","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":"The possibility of a strong $a$-theorem in six dimensions is examined in multi-flavor $\\phi^3$ theory. Contrary to the case in two and four dimensions, we find that in perturbation theory the relevant quantity $\\tilde{a}$ increases monotonically along flows away from the trivial fixed point. $\\tilde{a}$ is a natural extension of the coefficient $a$ of the Euler term in the trace anomaly, and it arises in any even spacetime dimension from an analysis based on Weyl consistency conditions. We also obtain the anomalous dimensions and beta functions of multi-flavor $\\phi^3$ theory to two loops. Our","authors_text":"Andreas Stergiou, Benjamin Grinstein, David Stone, Ming Zhong","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-06-13T20:00:01Z","title":"A challenge to the $a$-theorem in six dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3626","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:be737d6bae73b2242356149961580a77b73d866b5ce6b446d5e9251d570d0b3e","target":"record","created_at":"2026-05-18T02:18:04Z","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":"9fabd880e53fdbfd4c6db08a10be0cfef378977f2e15680c75abc21cf2c97cda","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-06-13T20:00:01Z","title_canon_sha256":"d182a708a340bbc75d6dc12f8e24578590d63a41ebdaf0cbad731d9f95cd40d9"},"schema_version":"1.0","source":{"id":"1406.3626","kind":"arxiv","version":2}},"canonical_sha256":"aba1b5f126eb944ded408b5db569d91077ecdf075d3a0cc20cbbff31de908106","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aba1b5f126eb944ded408b5db569d91077ecdf075d3a0cc20cbbff31de908106","first_computed_at":"2026-05-18T02:18:04.259194Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:18:04.259194Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8aPvjx3uP99k+2FJeLZ+cdIpgPBRnfMuCb728clYfcB00aCLhzhMDUz9k034UzRhE5GkpZO+FqS29mXAFWEvBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:18:04.259976Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.3626","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:be737d6bae73b2242356149961580a77b73d866b5ce6b446d5e9251d570d0b3e","sha256:4b2b9ee18907cb04cbe796daa73d88f25046c551583d6509f558f1a1fbecb09e"],"state_sha256":"10f85cab1379a71c662529e7e28ff2149a54fd9a114f2056ed34af8aea0d148f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zj8HT/zXPq2xRMYt1v8dk939TbABk4iqu436+taL6WdciGBDN6k2f18BfLuLSWhnmvWNatTlBYntIaf2yth6CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T10:02:17.639238Z","bundle_sha256":"d0ef69cb928151f1c8106f8c87947c8ec10d5f4dff23d81056fc5d739e314eef"}}