{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:BNECAUW5CGW765NY322DR7IILS","short_pith_number":"pith:BNECAUW5","canonical_record":{"source":{"id":"1405.7890","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-05-30T15:33:51Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"c1c47c2cd3f9247846648bf8f74d2ff8172dc37bc04a6f99fb1e10cb346b15be","abstract_canon_sha256":"50164f00d8cd2e806e9f661f3d8af1c886a1bdf612b229a677c2f01b13b96cea"},"schema_version":"1.0"},"canonical_sha256":"0b482052dd11adff75b8deb438fd085ca657fe3cdaba54a6eb365012575a81c7","source":{"kind":"arxiv","id":"1405.7890","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.7890","created_at":"2026-05-18T02:38:09Z"},{"alias_kind":"arxiv_version","alias_value":"1405.7890v2","created_at":"2026-05-18T02:38:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.7890","created_at":"2026-05-18T02:38:09Z"},{"alias_kind":"pith_short_12","alias_value":"BNECAUW5CGW7","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"BNECAUW5CGW765NY","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"BNECAUW5","created_at":"2026-05-18T12:28:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:BNECAUW5CGW765NY322DR7IILS","target":"record","payload":{"canonical_record":{"source":{"id":"1405.7890","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-05-30T15:33:51Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"c1c47c2cd3f9247846648bf8f74d2ff8172dc37bc04a6f99fb1e10cb346b15be","abstract_canon_sha256":"50164f00d8cd2e806e9f661f3d8af1c886a1bdf612b229a677c2f01b13b96cea"},"schema_version":"1.0"},"canonical_sha256":"0b482052dd11adff75b8deb438fd085ca657fe3cdaba54a6eb365012575a81c7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:09.774713Z","signature_b64":"Ya6nRKqm4EQ3E6s9SV/n51wRsDz/ADNsDzASHTv3v2oAFGeULuzKt0ku9yniLWfkWS9USWrjDrQ+DAUaxm/8Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0b482052dd11adff75b8deb438fd085ca657fe3cdaba54a6eb365012575a81c7","last_reissued_at":"2026-05-18T02:38:09.774069Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:09.774069Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.7890","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":"2026-05-18T02:38:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PhswpAa2s7ab1z14QSX9z4miV3Y6odzzrXUHe2Fmk0vgatdAkJ6Tin5ql0i3afH+XJ4mafpyvDa+7NoK/oFZBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T06:49:15.555981Z"},"content_sha256":"1ca8ed161432ede03582690817130485bcd311645e4327acb979fc27bd7e15ac","schema_version":"1.0","event_id":"sha256:1ca8ed161432ede03582690817130485bcd311645e4327acb979fc27bd7e15ac"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:BNECAUW5CGW765NY322DR7IILS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$\\mathbb{Z}_2$ Lattice Gerbe Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"cond-mat.stat-mech","authors_text":"Desmond A. Johnston","submitted_at":"2014-05-30T15:33:51Z","abstract_excerpt":"$2$-form abelian and non-abelian gauge fields on $d$-dimensional hypercubic lattices have been discussed in the past by various authors and most recently by Lipstein and Reid-Edwards. In this note we recall that the Hamiltonian of a $\\mathbb{Z}_2$ variant of such theories is one of the family of generalized Ising models originally considered by Wegner. For such \"$\\mathbb{Z}_2$ lattice gerbe theories\" general arguments can be used to show that a phase transition for Wilson surfaces will occur for $d>3$ between volume and area scaling behaviour. In $3d$ the model is equivalent under duality to a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.7890","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":"2026-05-18T02:38:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xBqxhmahi+gLtGNYHysD/ZPY6njLSF/twKJcd7Em3kDBVOhQvnp0miUgnQokShLRroHKAdgkTILYI01Blr3EDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T06:49:15.556329Z"},"content_sha256":"bafc9db96a201d331abed158c44b109404fa51127fb6c2166740193d58b39c15","schema_version":"1.0","event_id":"sha256:bafc9db96a201d331abed158c44b109404fa51127fb6c2166740193d58b39c15"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BNECAUW5CGW765NY322DR7IILS/bundle.json","state_url":"https://pith.science/pith/BNECAUW5CGW765NY322DR7IILS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BNECAUW5CGW765NY322DR7IILS/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":"2026-06-02T06:49:15Z","links":{"resolver":"https://pith.science/pith/BNECAUW5CGW765NY322DR7IILS","bundle":"https://pith.science/pith/BNECAUW5CGW765NY322DR7IILS/bundle.json","state":"https://pith.science/pith/BNECAUW5CGW765NY322DR7IILS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BNECAUW5CGW765NY322DR7IILS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:BNECAUW5CGW765NY322DR7IILS","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":"50164f00d8cd2e806e9f661f3d8af1c886a1bdf612b229a677c2f01b13b96cea","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-05-30T15:33:51Z","title_canon_sha256":"c1c47c2cd3f9247846648bf8f74d2ff8172dc37bc04a6f99fb1e10cb346b15be"},"schema_version":"1.0","source":{"id":"1405.7890","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.7890","created_at":"2026-05-18T02:38:09Z"},{"alias_kind":"arxiv_version","alias_value":"1405.7890v2","created_at":"2026-05-18T02:38:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.7890","created_at":"2026-05-18T02:38:09Z"},{"alias_kind":"pith_short_12","alias_value":"BNECAUW5CGW7","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"BNECAUW5CGW765NY","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"BNECAUW5","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:bafc9db96a201d331abed158c44b109404fa51127fb6c2166740193d58b39c15","target":"graph","created_at":"2026-05-18T02:38:09Z","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":"$2$-form abelian and non-abelian gauge fields on $d$-dimensional hypercubic lattices have been discussed in the past by various authors and most recently by Lipstein and Reid-Edwards. In this note we recall that the Hamiltonian of a $\\mathbb{Z}_2$ variant of such theories is one of the family of generalized Ising models originally considered by Wegner. For such \"$\\mathbb{Z}_2$ lattice gerbe theories\" general arguments can be used to show that a phase transition for Wilson surfaces will occur for $d>3$ between volume and area scaling behaviour. In $3d$ the model is equivalent under duality to a","authors_text":"Desmond A. Johnston","cross_cats":["hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-05-30T15:33:51Z","title":"$\\mathbb{Z}_2$ Lattice Gerbe Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.7890","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":"sha256:1ca8ed161432ede03582690817130485bcd311645e4327acb979fc27bd7e15ac","target":"record","created_at":"2026-05-18T02:38:09Z","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":"50164f00d8cd2e806e9f661f3d8af1c886a1bdf612b229a677c2f01b13b96cea","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-05-30T15:33:51Z","title_canon_sha256":"c1c47c2cd3f9247846648bf8f74d2ff8172dc37bc04a6f99fb1e10cb346b15be"},"schema_version":"1.0","source":{"id":"1405.7890","kind":"arxiv","version":2}},"canonical_sha256":"0b482052dd11adff75b8deb438fd085ca657fe3cdaba54a6eb365012575a81c7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0b482052dd11adff75b8deb438fd085ca657fe3cdaba54a6eb365012575a81c7","first_computed_at":"2026-05-18T02:38:09.774069Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:09.774069Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ya6nRKqm4EQ3E6s9SV/n51wRsDz/ADNsDzASHTv3v2oAFGeULuzKt0ku9yniLWfkWS9USWrjDrQ+DAUaxm/8Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:09.774713Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.7890","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1ca8ed161432ede03582690817130485bcd311645e4327acb979fc27bd7e15ac","sha256:bafc9db96a201d331abed158c44b109404fa51127fb6c2166740193d58b39c15"],"state_sha256":"88bf0bc0e4d0d343fb6a4cf869063050de27591aa7fdf22db0d44d59d071f76a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RHtUari4H8f0xYRXaJroGX2njxQXsNxyPA54Z3Id5kOaEWbz2hAT1XWBwyPu2dqdCy2J9cyc+wQR2j3BONMGDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T06:49:15.558235Z","bundle_sha256":"05f9976b2b918dd4d17c261249c86c081e123441940dfc2b5b8730d177cdc6a4"}}