{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:G56LTTPAJAEMB2UEQYOBDKAKHW","short_pith_number":"pith:G56LTTPA","canonical_record":{"source":{"id":"1509.05235","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-09-17T12:39:54Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"5f92dfc94f3fd43c16f1b16263cb418eb9092fae546077e238d1118b462a7a1f","abstract_canon_sha256":"e93cd9aae7b069a5fbfc4676c3bbdf1552d6204b3668bcae5583c0aca41d03de"},"schema_version":"1.0"},"canonical_sha256":"377cb9cde04808c0ea84861c11a80a3d876fd0cf6f53b88fdcd569df5fa97135","source":{"kind":"arxiv","id":"1509.05235","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.05235","created_at":"2026-05-18T01:16:48Z"},{"alias_kind":"arxiv_version","alias_value":"1509.05235v2","created_at":"2026-05-18T01:16:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.05235","created_at":"2026-05-18T01:16:48Z"},{"alias_kind":"pith_short_12","alias_value":"G56LTTPAJAEM","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"G56LTTPAJAEMB2UE","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"G56LTTPA","created_at":"2026-05-18T12:29:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:G56LTTPAJAEMB2UEQYOBDKAKHW","target":"record","payload":{"canonical_record":{"source":{"id":"1509.05235","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-09-17T12:39:54Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"5f92dfc94f3fd43c16f1b16263cb418eb9092fae546077e238d1118b462a7a1f","abstract_canon_sha256":"e93cd9aae7b069a5fbfc4676c3bbdf1552d6204b3668bcae5583c0aca41d03de"},"schema_version":"1.0"},"canonical_sha256":"377cb9cde04808c0ea84861c11a80a3d876fd0cf6f53b88fdcd569df5fa97135","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:48.619971Z","signature_b64":"QerWuAWyCydg4RG3T7XICizumvIQtqtvHaF/pu9BimBqvxkPINsAIyzWIGieivrYTrUk4KhFeFyCf9RSvMTcAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"377cb9cde04808c0ea84861c11a80a3d876fd0cf6f53b88fdcd569df5fa97135","last_reissued_at":"2026-05-18T01:16:48.619263Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:48.619263Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.05235","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":"2026-05-18T01:16:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"97FScCzOspG/8bjN6/ZZ3jwTgslt5t8lgOT9dmqwX8pRTJ8s9A+qXu5v9op56AKpVB9Upeb+YtlL87QO2jUBDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T06:11:13.487508Z"},"content_sha256":"83c67beee75852342fe7b866e5693d68aa7938a613504fe8fc1d6beb6b60861e","schema_version":"1.0","event_id":"sha256:83c67beee75852342fe7b866e5693d68aa7938a613504fe8fc1d6beb6b60861e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:G56LTTPAJAEMB2UEQYOBDKAKHW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"QCD Breaks Lorentz Invariance and Colour","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"A. P. Balachandran","submitted_at":"2015-09-17T12:39:54Z","abstract_excerpt":"In a previous work [1], we have argued that the algebra of non-abelian superselection rules is spontaneously broken to its maximal abelian subalgebra, that is, the algebra generated by its completing commuting set (the two Casimirs and a basis of its Cartan subalgebra). In this paper, alternative arguments confirming these results are presented. In addition, Lorentz invariance is shown to be broken in QCD, just as it is in QED. The experimental consequences of these results include fuzzy mass and spin shells of coloured particles like quarks, and decay life times which depend on the frame of o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.05235","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":"2026-05-18T01:16:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LQio8PdiiApkvAVGYMH5jbXRJKbjRvzSwOGL1c/d7F9x3c++rdzB5SQA9VoWN9CRkOhqrnEOUYblEvVxc2k4Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T06:11:13.487872Z"},"content_sha256":"ec22636416a59a0f73f9cba4803809b8670018d338dc72322d582a349f89f6c0","schema_version":"1.0","event_id":"sha256:ec22636416a59a0f73f9cba4803809b8670018d338dc72322d582a349f89f6c0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G56LTTPAJAEMB2UEQYOBDKAKHW/bundle.json","state_url":"https://pith.science/pith/G56LTTPAJAEMB2UEQYOBDKAKHW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G56LTTPAJAEMB2UEQYOBDKAKHW/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":"2026-06-12T06:11:13Z","links":{"resolver":"https://pith.science/pith/G56LTTPAJAEMB2UEQYOBDKAKHW","bundle":"https://pith.science/pith/G56LTTPAJAEMB2UEQYOBDKAKHW/bundle.json","state":"https://pith.science/pith/G56LTTPAJAEMB2UEQYOBDKAKHW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G56LTTPAJAEMB2UEQYOBDKAKHW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:G56LTTPAJAEMB2UEQYOBDKAKHW","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":"e93cd9aae7b069a5fbfc4676c3bbdf1552d6204b3668bcae5583c0aca41d03de","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-09-17T12:39:54Z","title_canon_sha256":"5f92dfc94f3fd43c16f1b16263cb418eb9092fae546077e238d1118b462a7a1f"},"schema_version":"1.0","source":{"id":"1509.05235","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.05235","created_at":"2026-05-18T01:16:48Z"},{"alias_kind":"arxiv_version","alias_value":"1509.05235v2","created_at":"2026-05-18T01:16:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.05235","created_at":"2026-05-18T01:16:48Z"},{"alias_kind":"pith_short_12","alias_value":"G56LTTPAJAEM","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"G56LTTPAJAEMB2UE","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"G56LTTPA","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:ec22636416a59a0f73f9cba4803809b8670018d338dc72322d582a349f89f6c0","target":"graph","created_at":"2026-05-18T01:16:48Z","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 a previous work [1], we have argued that the algebra of non-abelian superselection rules is spontaneously broken to its maximal abelian subalgebra, that is, the algebra generated by its completing commuting set (the two Casimirs and a basis of its Cartan subalgebra). In this paper, alternative arguments confirming these results are presented. In addition, Lorentz invariance is shown to be broken in QCD, just as it is in QED. The experimental consequences of these results include fuzzy mass and spin shells of coloured particles like quarks, and decay life times which depend on the frame of o","authors_text":"A. P. Balachandran","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-09-17T12:39:54Z","title":"QCD Breaks Lorentz Invariance and Colour"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.05235","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":"sha256:83c67beee75852342fe7b866e5693d68aa7938a613504fe8fc1d6beb6b60861e","target":"record","created_at":"2026-05-18T01:16:48Z","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":"e93cd9aae7b069a5fbfc4676c3bbdf1552d6204b3668bcae5583c0aca41d03de","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-09-17T12:39:54Z","title_canon_sha256":"5f92dfc94f3fd43c16f1b16263cb418eb9092fae546077e238d1118b462a7a1f"},"schema_version":"1.0","source":{"id":"1509.05235","kind":"arxiv","version":2}},"canonical_sha256":"377cb9cde04808c0ea84861c11a80a3d876fd0cf6f53b88fdcd569df5fa97135","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"377cb9cde04808c0ea84861c11a80a3d876fd0cf6f53b88fdcd569df5fa97135","first_computed_at":"2026-05-18T01:16:48.619263Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:48.619263Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QerWuAWyCydg4RG3T7XICizumvIQtqtvHaF/pu9BimBqvxkPINsAIyzWIGieivrYTrUk4KhFeFyCf9RSvMTcAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:48.619971Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.05235","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:83c67beee75852342fe7b866e5693d68aa7938a613504fe8fc1d6beb6b60861e","sha256:ec22636416a59a0f73f9cba4803809b8670018d338dc72322d582a349f89f6c0"],"state_sha256":"1911f0a740afaaf3e18adcc9fca769ec11c4d0e6b126dccc9f1f6d79c89e33e5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mZRcLr7dhDpa0sc5u+m7R5JgFGA3Uu/EEej2smktONZpJGmqNcPnp0JcXjUowHQOpDcgco7Gewxbn8ATBDn7DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T06:11:13.489883Z","bundle_sha256":"90e5796100dcecaa3921444c751b2f075d8d6060b90ee3b3171fbb5ffe90b37f"}}